Alcuni recenti sviluppi nei problemi 19-simo e 20-simo di Hilbert

Bollettino della Unione Matematica Italiana A

Volumn 7, Issue SUPPL. 11 part 2, 1997, Pages 323-352

  Marcellini, Paolo ^a  

^a UNIVERSITY OF FLORENCE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0347799696     PISSN: 03924033     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (222)

1. E. ACERBI - N. FUSCO, Semicontinuity problems in the calculus of variations, Arch. Rational Mech. Anal., 86 (1984), 125-145.
2. E. ACERBI - N. FUSCO, A regularity theorem for minimizers of quasiconvex integrals, Arch. Rational Mech. Anal., 99 (1987), 261-281.
3. E. ACERBI - N. FUSCO, Partial regularity under anisotropic (p,q) growth conditions, J. Differential Equations 107 (1994), 46-67.
4. R. A. ADAMS, Sobolev spaces, Academic Press, New York, 1975.
5. L. AMBROSIO, New lower semicontinuity results for integral functionals, Rend. Accad. Naz. Sci. XL, 11 (1987), 1-42.
6. C. ARZELÁ, Sul principio di Dirichlet, Rend. Accad. Sci. Ist Bologna, 1 (1896-97), 71-84.
7. G. AUBERT - R. TAHRAOUI, Thérèmes d'existence pour des problèmes du calcul des variations, J. Differential Eq., 33 (1979), 1-15.
8. G. AUBERT - R. TAHRAOUI, Théorèmes d'existence en optimimisation non convexe, Appl. Anal., 18 (1984), 75-100.
9. J. M. BALL, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rat. Mech. Anal., 63 (1977), 337-403.
10. J. M. BALL - R. D. JAMES, Fine phase mixtures as minimizers of energy, Arch. Rat. Mech. Anal., 100 (1987), 15-52.
11. J. M. BALL - R.D. JAMES, Proposed experimental tests of a theory of fine microstructure and the two well problem, Philos. Trans. Royal. Soc. London, A338 (1991), 389-450.
12. M. BARDI - I. CAPUZZO DOLCETTA, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations, libro in preparazione.
13. G. BARLES, Solutions de viscosite des equations de Hamilton-Jacobi, Mathematiques and Applications, 17, Springer-Verlag, Berlin, 1994.
14. P. BAUMAN - D. PHILLIPS, A nonconvex variational problem related to change of phase, J. Appl. Math. Optimization, 21 (1990), 113-138.
15. A. BENSOUSSAN - J. L. LIONS - G. PAPANICOLAOU, Asymptotic analysis for periodic structures, North-Holland, Amsterdam, 1978.
16. S. H. BENTON, The Hamilton Jacobi equation. A global approach, Academic Press, New York, 1977.
17. L. D. BERKOWITZ, Lower semicontinuity of integral functionals, Trans. Am. Math. Soc., 192 (1974), 51-57.
18. S. BERNSTEIN, Sur la nature analytique des solutions des équations aux derivées partielles du second ordre, Math. Annalen, 59 (1904), 20-76.
19. 2,2 regularity for weak solutions of elliptic systems with nonstandard growth, J. Math. Anal. Applications, 176 (1993), 224-234.
20. L. BOCCARDO - B. DACOROGNA, Monotonicity of certain differential operators in divergence form, Manuscripta Math., 64 (1989), 253-260.
21. 1, Differential and Integral Equations, 9 (1996), 209-212.
22. ∞-regularity for variational problems with sharp non standard growth conditions, Boll. Un. Mat. Ital., 4-A (1990), 219-225.
23. E. BOMBIERI, Variational problems and elliptic equations (Hilbert's problem 20), Proc. Symposia Pure Math., Vol. XXVIII, F. E. Browder Editor, American Math. Society, 1976, 525-535.
24. H. BREZIS, Analyse fonctionnelle, Théorie et applications, Masson, Paris, 1983.
25. F. E. BROWDER, Mathematical developments arising from Hilbert problems, Proc. Symposia Pure Math., Vol. XXVIII, American Math. Society, 1976.
26. G. BUTTAZZO, Semicontinuity, relaxation, and integral representation in the calculus of variations, Pitman Research Notes in Math., 207, Longman, Harlow, 1989.
27. G. BUTTAZZO, V. FERONE - B. KAWOHL, Minimum problems over sets of concave functions and related questions, Math. Nachrichten, 173 (1995), 71-89.
28. R. CACCIOPPOLI, Sulle equazioni ellittiche a derivate parziali con n variabili indipendenti, Rend. Accad. Naz. Lincei, 19 (1934), 83-89.
29. R. CACCIOPPOLI, Limitazioni integrali per le soluzioni di un'equazione lineare ellittica a derivate parziali, Giornale Mat. Battaglini, 80 (1950-51), 186-212.
30. R. CACCIOPPOLI - G. SCORZA DRAGONI, Necessità della condizione di Weierstrass per la semicontinuità di un integrale doppio sopra una data superficie, Memorie Acc. d'Italia, 9 (1938), 251-268.
31. J.W. CALKIN, Functions of several variables and absolute continuity (I), Duke Math. J., 6 (1940), 170-185.
32. I. CAPUZZO DOLCETTA - L. C. EVANS, Optimal switching for ordinary differential equations, SIAM J. Optim. Control, 22 (1988), 1133-1148.
33. I. CAPUZZO DOLCETTA - P. L. LIONS, Viscosity solutions of Hamilton-Jacobi equations and state-constraint problem, Trans. Amer. Math. Soc., 318 (1990), 643-683.
34. C. CARATHEODORY, Calculus of variations and partial differential equations of the first order, Holden Day, San Francisco, 1965.
35. P. CELADA - G. DAL MASO, Further remarks on the lower semicontinuity of polyconvex integrals, Ann. Inst. Henri Poincaré, Anal. Non Lin., 11 (1994), 661-691.
36. A. CELLINA, On the differential inclusion x′ ∈ [-1,1], Atti Accad. Naz. Lincei, Rend. Sc. Fis. Mat. Nat., 69 (1980), 1-6.
37. A. CELLINA, On minima of a functional of the gradient: necessary conditions, Nonlinear Analysis. Theory Meth. Appl., 20 (1993), 337-341.
38. A. CELLINA, On minima of a functional of the gradient: sufficient conditions, Nonlinear Analysis. Theory Meth. Appl., 20 (1993), 343-347.
39. A. CELLINA - G. COLOMBO, On a classical problem of the calculus of variations without convexity assumptions, Ann. Inst. Henri Poincaré, Anal. Non Lin., 7 (1990), 97-106.
40. A. CELLINA - S. ZAGATTI, An existence result in a problem of the vectorial case of the calculus of variations, S.I.A.M. J. Control Optimization, 33 (1955), 960-970.
41. L. CESARI, Lower semicontinuity and lower closure theorems without seminormality conditions, Ann. Mat. Pura Appl., 98 (1974), 381-397.
42. L. CESARI, An existence theorem without convexity conditions, SIAM J. Control, 12 (1974), 319-331.
43. L. CESARI, Optimization - Theory and applications, Appl. Math. 17, Springer-Verlag, 1983.
44. M. CHIPOT - L. C. EVANS, Linearization at infinity and Lipschitz estimates for certain problems in the calculus of variations, Proc. Royal Soc. Edinburgh, 102A (1986), 291-303.
45. M. CHIPOT - D. KINDERLEHRER, Equilibrium configurations of crystals, Arch. Rational Mech. Anal., 103 (1988), 237-277.
46. H. J. CHOE, Interior behaviour of minimizers for certain functionals with nonstandard growth, Nonlinear Anal. Theory Methods Appl., 19 (1992), 933-945.
47. M. G. CRANDALL - L. C. EVANS - P. L. LIONS, Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc., 282 (1984), 487-502.
48. M. G. CRANDALL - H. ISHII - P.L. LIONS, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc., 27 (1992), 1-67.
49. M. G. CRANDALL - P. L. LIONS, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc., 277 (1983), 1-4.
50. A. CUTRÌ, Some remarks on Hamilton-Jacobi equations and non convex minimization problems, Rendiconti Mat., 13 (1993), 733-749.
51. B. DACOROGNA, A relaxation theorem and its applications to the equilibrium of gases, Arch. Rational Mech. Anal., 77 (1981), 359-386.
52. B. DACOROGNA, Direct methods in the calculus of variations, Applied Math. Sciences, 78, Springer-Verlag, 1989.
53. B. DACOROGNA - P. MARCELLINI, Semicontinuité pour des intégrands polyconvexes sans continuité des determinants, C. R. Acad. Sci. Paris, Série I. Math., 311 (1990), 393-396.
54. B. DACOROGNA - P. MARCELLINI, Existence of minimizers for non quasiconvex integrals, Arch. Rational Mech. Anal., 131 (1995), 359-399.
55. B. DACOROGNA - P. MARCELLINI, Théorèms d'existence dans les cas scalaire et vectoriel pour les équations de Hamilton-Jacobi, C. R. Acad. Sci. Paris, 322 (1996), 237-240.
56. B. DACOROGNA - P. MARCELLINI, General existence theorems for Hamilton-Jacobi equations in the scalar and vectorial cases, Acte Mathematica, 178 (1997), 1-37.
57. B. DACOROGNA - P. MARCELLINI, Sur le problème de Cauchy-Dirichlet pour les systèmes d'équations non linéaires du premier ordre, C. R. Acad. Sci. Paris, 323 (1996), 599-602.
58. B. DACOROGNA - P. MARCELLINI, Cauchy-Dirichlet problem for first order nonlinear systems, preprint gennaio 1997.
59. A. DALL'AGLIO - E. MASCOLO - G. PAPI, Local boundedness for minima with non standard growth conditions, Rend. Mat., inviato per la pubblicazione.
60. G. DAL MASO, An introduction to Γ-convergence, Progress in Nonlinear Differential Equat. and their Appl., Vol. 8, Birkhauser, Boston, 1993.
61. G. DAL MASO - L. MODICA, A general theory of variational functionals, Topics in Funct. Analysis 1980-81, Quaderni della Scuola Normale Sup. di Pisa, 1982.
62. G. DAL MASO - C. SBORDONE, Weak lower semicontinuity of polyconvex integrals: a bordeline case, Math. Z., 218 (1995), 603-609.
63. R. DE ARCANGELIS - F. SERRA CASSANO, On the homogenization of degenerate elliptic equations in divergence form, J. Math. Pures Appl., 71 (1992), 119-138.
64. F. S. DE BLASI - G. PIANIGIANI, A Baire category approach to the existence of solutions of multivalued differential equations in Banch spaces; Funkcialaj Ekvacioj, 25 (1982), 153-162.
65. F. S. DE BLASI - G. PIANIGIANI, Non convex valued differential inclusions in Banach spaces, J. Math. Anal. Appl., 157 (1991), 469-494.
66. E. DE GIORGI, Sulla differenziabilità e l'analiticità degli estremali degli integrali multipli regolari, Mem. Accad. Sci. Torino, Cl. Sci. Fis. Mat. Nat., 3 (1957), 25-43.
67. E. DE GIORGI, Un esempio di estremali discontinue per un problema variazionale di tipo ellittico, Boll. Un. Mat. Ital., 1 (1968), 135-137.
68. E. DE GIORGI, Teoremi di semicontinuità nel calcolo delle variazioni, Ist. Naz. Alta Mat. Roma, 1968-69.
69. E. DE GIORGI, Sulla convergenza di alcune successioni di integrali del tipo dell'area, Rend. Mat., 8 (1975), 277-294.
70. 1+α local regularity of weak solutions of degenerate elliptic equations, Nonlinear Anal. Theory Methods Appl., 7 (1983), 827-850.
71. A. L. DONTCHEV - T. ZOLEZZI, Well posed optimization problems, Lecture Notes in Math., 1543, Springer-Verlag, Berlin, 1993.
72. A. DOUGLIS, The continuous dependence of generalized solutions of non linear partial differential equations upon initial data, Comm. Pure Appl. Math., 14 (1961), 267-284.
73. D.M. DUC - J. EELLS, Regularity of exponentially harmonic functions, Int. J. Math., 2 (1991), 395-408.
74. I. EKELAND, Discontinuités de champs hamiltoniens et existence de solutions optimales en calcul des variations, Publ. Math. (IHES), 47 (1977), 5-32.
75. I. EKELAND - R. TEMAM, Analyse convexe et problemes variationnels, Dunod Gauthier-Villars, Paris, 1974.
76. 1,α regularity for solutions of certain degenerate elliptic p.d.e., J. Differential Equations, 45 (1982), 356-373.
77. L. C. EVANS, Quasiconvexity and partial regularity in the calculus of variations, Arch. Rational Mech. Anal., 95 (1986), 227-252.
78. E. B. FABES - C. E. KENIG - R. SERAPIONI, The local regularity of solutions of degenerate elliptic equations, Comm. Partial Differential Equations, 7 (1982), 77-116.
79. N. B. FIROOZYE - R. V. KOHN, Geometric parametres and the relaxation of multiwell energies, in Microstructure and phase transition, edited by D. Kinderlehrer et al., Springer, 1992.
80. W. H. FLEMING - H. M. SONER, Controllated Markov processes and viscosity solutions. Applications of Mathematics, Springer-Verlag, Berlin, 1993.
81. I. FONSECA, Variational methods for elastic crystals, Arch. Rat. Mech. Anal., 97 (1987), 189-220.
82. I. FONSECA - J. MALÝ, Relaxation of multiple integrals below the growth exponent, Ann. Inst. Henri Poincaré, Anal. Non Lin., in corso di stampa.
83. I. FONSECA - P. MARCELLINI, Relaxation of multiple integrals in subcritical Sobolev spaces, J. Geom. Anal., in corso di stampa.
84. I. FONSECA - L. TARTAR, The gradient theory of phase transition for systems with two potential wells, Proc. Royal Soc. Edinburgh, 111A (1989), 89-102.
85. G. FRIESECKE, A necessary and sufficient condition for nonattainment and formation of microstructure almost everywhere in scalar variational problems, Proc. Royal Soc. Edinburgh, 124 (1994), 437-471.
86. 1,α partial regularity of functions minimizing quasiconvex integrals, Manuscripta Math., 54 (1985), 121-143.
87. N. FUSCO - J. HUTCHINSON, A direct proof for lower semicontinuity of polyconvex functionals, Manuscripta Math., 85 (1995), 35-50.
88. N. FUSCO, P. MARCELLINI - A. ORNELAS, Existence of minimizers for some nonconvex one-dimensional integrals, Portugaliae Mathematica, in corso di stampa.
89. N. FUSCO - C. SBORDONE, Higher integrability of the gradient of minimizers of functional with nonstandard growth conditions, Comm. Pure Appl. Math., 43 (1990), 673-683.
90. N. FUSCO - C. SBORDONE, Local boundedness of minimizers in a limit case, Manuscripta Math., 69 (1990), 19-25.
91. N. FUSCO - C. SBORDONE, Some remarks on the regularity of minima of anisotropic integrals, Comm. on P.D.E., 18 (1993), 153-167.
92. W. GANGBO, On the weak lower semicontinuity of energies with polyconvex integrands, J. Math. Pures Appl., 73(1994), 455-469.
93. p-integrability of the partial derivatives of a quasi conformal mapping, Acta Math., 130 (1973), 265-277.
94. D. GIACHETTI - R. SCHIANCHI, Minima of some non convex non coercive problems, Ann. Mat. Pura Appl., 165 (1993), 109-120.
95. M. GIAQUINTA, Multiple integrals in the calculus of variations and nonlinear elliptic systems, Ann. Math. Studies, 105, Princeton Univ. Press, 1983.
96. M. GIAQUINTA, Growth conditions and regularity, a counterexample, Manuscripta Math., 59 (1987), 245-248.
97. M. GIAQUINTA - E. GIUSTI, On the regularity of the minima of variational integrals, Acta Math., 148 (1982), 31-46.
98. M. GIAQUINTA - E. GIUSTI, Q-minima, Ann. Inst. Henri Poincaré, Anal. Non Lin., 1 (1984), 79-107.
99. M. GIAQUINTA - S. HILDEBRANDT, Calculus of variations I and II, Grundlehren der Math. Wiss, 310-311, Springer, Berlin, 1996.
100. M. GIAQUINTA - G. MODICA, Regularity results for some classes of higher order nonlinear elliptic systems, J. Reine Angw. Math., 311/312 (1979), 145-169.
101. M. GIAQUINTA - G. MODICA, Remarks on the regularity of the minimizers of certain degenerate functional, Manuscripta Math., 57 (1986), 55-99.
102. M. GIAQUINTA - G. MODICA - J. SOUČEK, Cartesian currents, weak diffeomorphisms and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal., 106 (1989), 97-159; Erratum and addenda, 109 (1990), 385-392.
103. D. GILBARG - N.S. TRUDINGER, Elliptic partial differential equations of second order, Grundl. der Math. Wiss., 224, Springer-Verlag, Berlin, Heidelberg, New York, 1977.
104. E. GIUSTI, Regolarità parziale delle soluzioni di sistemi ellittici quasi lineari di ordine arbitrario, Ann. Sc. Norm. Sup. Pisa, 23 (1969), 115-141.
105. E. GIUSTI, Equazioni ellittiche del secondo ordine, Quaderni Unione Matematica Italiana, No. 6, Pitagora, Bologna, 1978.
106. E. GIUSTI, Minimal surfaces and functions of bounded variation, Birkhäuser, Boston, 1984.
107. E. GIUSTI, Metodi diretti nel calcolo delle variazioni, Unione Matematica Italiana, Bologna, 1994.
108. E. GIUSTI - M. MIRANDA, Un esempio di soluzioni discontinue per un problema di minimo relativo ad un integrale regolare del calcolo delle variazioni, Boll. Un. Mat. Ital., 2 (1968), 1-8.
109. E. GIUSTI - M. MIRANDA, Sulla regolarità delle soluzioni deboli di una classe di sistemi ellittici quasi-lineari, Arch. Rat. Mech. Anal., 31 (1968), 173-184.
110. G. GOFFMAN - J. SERRIN, Sublinear functions of measures and variational integrals, Duke Math. J., 31 (1964), 159-178.
111. M.E. GURTIN - R. TEMAM, On the anti-plane shear problem infinite elasticity, J. Elasticity, 11 (1981), 197-206.
112. HONG MIN-CHUN, Existence and partial regularity in the calculus of variations, Ann. Mat. Pura Appl., 149 (1987), 311-328.
113. HONG MIN-CHUNG, Some remarks on the minimizers of variational integrals with non standard growth conditions, Boll. Un. Mat. Ital., 6-A (1992), 91-101.
114. E. HOPE, Zum analytischen Charakter der Lösungen regulärer zweidimensionaler Variationsprobleme, Math. Z., 30 (1929), 404-413.
115. A. D. IOFFE, On lower semicontinuity of integral functionals I, SIAM J. Control Optimization, 15 (1977), 521-538.
116. A. V. IVANOV, Quasilinear degenerate and non uniformly elliptic and parabolic equations of second order, Proc. Steklov Inst. Math., Russian tom 160 (1982), American Math. Soc., Providence, 1984.
117. D. KINDERLHERER - G. STAMPACCHIA, Introduction to variational inequalities and their applications, Academic Press, New York, 1980.
118. D. KINDERLEHRER - P. PEDREGAL, Remarks about the analysis of gradient Young measures, Proc. Partial Differential Equations and Related Subjects, Miranda M. Ed., Pitman Research Notes in Math., 262 (1992), Longam, 125-150.
119. R.V. KOHN, The relaxation of a double-well energy, Continuum Mech. Thermodynamics, 3 (1991), 918-1000.
120. R. V. KOHN - G. STRANG, Optimal design and relaxation of variational problems I, II, III, Commun. Pure Appl. Math., 39 (1986), 113-137, 139-182, 353-377.
121. A. G. KOROLEV, On the boundedness of generalized solutions of elliptic differential equations with nonpower nonlinearities, Mat. Sb., 180 (1989), 78-100; Math. USSR-Sb., 66 (1990), 83-106.
122. A. G. KOROLEV, On the boundedness of generalized solutions of elliptic differential equations with nonpower nonlinearities, Mat. Sb., 180 (1989), 78-100; Math. USSR-Sb., 66 (1990), 83-106.
123. S. N. KRUZKOV, Generalized solutions of Hamilton-Jacobi equation of eikonal type, USSR Sbornik, 27 (1975), 406-446.
124. O. LADYZHENSKAYA - N. URAL'TSEVA, Linear and quasilinear elliptic equations, Math. in Science and Engineering, Vol., 46, Academic Press, San Diego, 1968.
125. O. LADYZHENSKAYA - N. URAL'TSEVA, Local estimates for gradients of solutions of non-uniformly elliptic and parabolic equations, Comm. Pure Appl. Math, 23 (1970), 677-703.
126. P.D. LAX, Hyperbolic systems of conservation laws II, Comm. Pure Appl. Math., 10 (1957), 537-566.
127. H. LEBESGUE, Intégrale, longueur, aire, Ann. Mat. Pura Appl., 7 (1902), 231-359.
128. F. LEONETTI, Two-dimensional regularity of minima of variational functionals without standard growth conditions, Ricerche di Matematica, 38 (1989), 41-50.
129. F. LEONETTI, Weak differentiability for solutions to nonlinear elliptic systems with p,q-growth conditions, Ann. Mat. Pura Appl., 162 (1992), 349-366.
130. J. LERAY - J. SCHAUDER, Topologie et équations fonctionnelles, Ann. Sci. Ec. Norm. Sup., 51 (1934), 45-78.
131. J. LEWIS, Regularity of derivatives of solutions to certain degenerate elliptic equations, Indiana Univ. Math. J., 32 (1983), 849-858.
132. L. LICHTENSTEIN, Über den analytischen charakter der lösungen zweidimensionaler variations probleme, Bull. Acad. Sci. Cracoviae, 1912.
133. G. M. LIEBERMAN, On the regularity of the minimizer of a functional with exponential growth, Comment. Math. Univ. Carolin., 33 (1992), 45-49.
134. G. M. LIEBERMAN, Gradient estimates for a class of elliptic systems, Ann. Mat. Pura Appl., 164 (1993), 103-120.
135. J. L. LIONS - E. MAGENES, Non-homogeneous boundary value problems and applications I, II, III, Springer-Verlag, 1972.
136. P.L. LIONS, Generalized solutions of Hamilton-Jacobi equations, Research Notes in Math., no. 69, Pitman, London,1982.
137. J. MALÝ, Weak lower semicontinuity of polyconvex integrals, Proc. Royal Soc. Edinburgh, 123A (1993), 681-691.
138. J. MALÝ, Weak lower semicontinuity of quasiconvex integrals, Manuscripta Math., 85 (1994), 419-428.
139. J. J. MANFREDI, Regularity for minima of functional with p-growth, J. Differential Equations, 76 (1988), 203-212.
140. P. MARCELLINI, Alcune osservazioni sull'esistenza del minima di integrali del calcolo delle variazioni senza ipotesi di convessità, Rendiconti di Matematica, 13 (1980), 271-281.
141. P. MARCELLINI, A relation between existence of minima for nonconvex integrals and uniqueness for non strictly convex integrals of the calculus of variations, in Mathematical Theories of Optimization, Proceedings edited by J. P. Cecconi and T. Zolezzi, Lecture Notes in Math., vol. 979, Springer, 1983, 216-231.
142. P. MARCELLINI, Some remarks on uniqueness in the calculus of variations, Collège de France Seminar, edited by H. Brézis and J. L. Lions, Research Notes in Math., vol., 84, Pitman, 1983, 148-153.
143. P. MARCELLINI, Approximation of quasiconvex functions and lower semicontinuity of multiple integrals, Manuscripta Math., 51 (1985), 1-28.
144. P. MARCELLINI, On the defininition and the lower semicontinuity of certain, quasi-convex integrals, Ann. Inst. H. Poincare, Anal. Non. Lin., 3 (1986), 385-392.
145. P. MARCELLINI, Un exemple de solution discontinue d'un problèeme variationnel dans le cas scalaire, Istituto Matematico «U. Dini», No. 11, Università di Firenze, 1987.
146. P. MARCELLINI, Regularity of minimizers of integrals of the calculus of variations with non standard growth conditions, Arch. Rational Mech. Anal., 105 (1989), 267-284.
147. P. MARCELLINI, Non convex integrals of the calculus of variations, in Methods of nonconvex analysis, edited by A. Cellina, Lecture Notes in Math., vol. 1446, Springer, 1990, 16-57.
148. P. MARCELLINI, Regularity and existence of solutions of elliptic equations with p,q-growth conditions, J. Differential Equations, 90 (1991), 1-30.
149. P. MARCELLINI, Regularity far elliptic equations with general growth conditions, J. Differential Equations, 105 (1993), 296-333.
150. P. MARCELLINI, Everywhere regularity for a class of elliptic systems without growth conditions, Ann. Scuola Norm. Sup. Pisa, 23 (1996), 1-25.
151. P. MARCELLINI - C. SBORDONE, Semicontinuity problems in the calculus of variations, Nonlinear Anal., Theory Meth. Appl., 4 (1980), 241-257.
152. P. MARCELLINI - C. SBORDONE, On the existence of minima of multiple integrals of the calculus of variations, J. Math. Pures Appl., 62 (1983), 1-9.
153. E. MASCOLO, Some remarks on non-convex problems, in Material instabilities in continuum mechanics, edited by J. M. Ball, Calderon Press, Oxford, 1988, 269-286.
154. E. MASCOLO - G. PAPI, Local boundedness of minimizers of integrals of the calculus of variations, Ann. Mat. Pura Appl., 167 (1994), 323-339.
155. E. MASCOLO - R. SCHIANCHI, Existence theorems for nonconvex problems, J. Math. Pures Appl., 62 (1983), 349-359.
156. E. MASCOLO - R. SCHIANCHI, Nonconvex problems of the calculus of variations, Nonlinear Anal., 9 (1985), 371-379.
157. E. MASCOLO - R. SCHIANCHI, Existence theorems in the calculus of variations, J. Differential Eq., 67 (1987), 185-198.
158. B. J. MCSHANE, On the necessary condition of Weierstrass in the multiple integral problem of the calculus of variations, Ann. Math., 32 (1931), 578-590.
159. N. MEYERS, Quasiconvexity and lower semicontinuity of mulitple integrals of any order, Trans. Amer. Math. Soc., 119 (1965), 126-149.
160. M. MIRANDA, Recenti progressi nel calcolo delle variazioni, Boll. Un. Mat. Ital., 17-A (1980), 209-225.
161. L. MODICA - S. MORTOLA, Un esempio di Γ-convergenza, Boll. Un. Mat. Ital., 14-B (1977), 285-299.
162. M. D. P. MONTEIRO MARQUES - A. ORNELAS, Genericity and existence of a minimum for scalar integral functionals, J. Optim. Th. Appl., 86 (1995), 421-431.
163. C. B. MORREY, On the solutions of quasi-linear elliptic partial diffrential equations, Trans. Amer. Math. Soc., 43 (1938), 126-166.
164. C. B. MORREY, Functions of several variables and absolute continuity (II), Duke Math. J., 6 (1940), 187-213.
165. C. B. MORREY, Quasi-convexity and the lower semicontinuity of multiple integrals, Pacific J. Math., 2 (1952), 25-53.
166. C. B. MORREY, On the analyticity of the solutions of analytic nonlinear elliptic systems of partial differential equations I, II, Amer. J. Math., 80 (1958), 198-218, 219-234.
167. C. B. MORREY, Multiple integrals in the calculus of variations, D. Grundl. Math. Wiss., 130, Springer-Verlag, 1966.
168. C. B. MORREY, Partial regularity results for non-linear elliptic systems, J. Math. Mech., 17 (1968), 649-670.
169. G. MOSCARIELLO - L. NANIA, Hölder continuity of minimizers of functionals with non standard growth conditions, Ricerche di Matematica, 40 (1991), 259-273.
170. J. MOSER, A new proof of De Giorgi's theorem concerning the regularity problem for elliptic differential equations, Comm. Pure Appl. Math, 13 (1960), 457-468.
171. S. MÜLLER, Weak continuity of determinants and nonlinear elasticity, C.R. Acad. Sc. Paris, 307 (1988), 501-506.
172. S. MÜLLER, Minimizing sequences for nonconvex functionals, phase transitions and singular perturbations, Lecture Notes in Physics, Springer, 1990, 31-44.
173. S. MÜLLER - V. SVERAK, Attainment results for the two-well problem by convex integration, J. JOST Ed., International Press, 1996, 239-251.
174. F. MURAT, Compacité par compensation, II, Proc. Internat. Meeting on Recent Methods in Nonlinear Analysis, edited by De Giorgi, Magenes, Mosco, Pitagora, Bologna, (1979), 245-256.
175. J. NASH, Continuity of solutions of parabolic and elliptic equations, Amer. J. Math., 8 (1958), 931-954.
176. J. NEČAS, Example of an irregular solution to a nonlinear elliptic system with analytic coefficients and conditions for regularity, Theory of Nonlinear Operators, Abhandlungen der Akad. der Wissen. der DDR, 1977. Proc. of a Summer School held in Berlin in 1975.
177. L. NIRENBERG, Remarks on strongly elliptic partial differential equations, Comm. Pure Appl. Math., 8 (1955), 648-674.
178. C. OLECH, Integrals of set valued functions and linear optimal control problems, Colloque sur la théorie mathématique du contrôle optimal, C.B.R.M., Vander Louvain, 1970, 109-125.
179. 1-weak lower semicontinuity of integral functionals, Bull. Polish. Acad. Sci. Math., 25 (1977), 135-142.
180. L. PEPE, Leonida Tonelli e il calcolo delle variazioni, in La matematica tra le due guerre, Bologna, Pitegora, 1987, 307-317.
181. I. PETROWSKY, Sur l'analyticité des solutions des systèmes d'équations différentielles, Rec. Math. N. S. Mat. Sbornik, 5 (1939), 3-70.
182. C. PUCCI, Operatori ellittici estremanti, Ann. Mat. Pura Appl., 65 (1964), 311-327.
183. J. P. RAYMOND, Champs hamiltoniens, relaxation et existence de solutions en calcul des variations, J. Differential Eq., 70 (1987), 226-274.
184. J. P. RAYMOND, Théorème d'existence pour des problèmes variationnels non convexes, Proc. Royal Soc. Edinburgh, 107A (1987), 43-64.
185. J. P. RAYMOND, Lipschitz regularity of solutions of some asymptotically convex problems, Proc. Royal Soc. Edinburgh, 117A (1991), 59-73.
186. J. P. RAYMOND, Existence of minimizers for vector problems without quasiconvexity condition, Nonlinear Anal., Theory, Methods Appl., 18 (1992), 815-828.
187. R. T. ROCKAFELLAR, Convex analysis, Princeton Univ. Press, Princeton, 1970.
188. R. T. ROCKAFELLAR, Integral functionals, normal integrands and measurable selections, in Nonlinear operators and the calculus of variations, edited by Gossez et al., Lecture Notes in Math., 543, Sringer, Berlin, 1975, 157-207.
189. H. RUND, The Hamilton-Jacobi theory in the calculus of variations, Van Nostrand, Princeton, 1966.
190. C. SBORDONE, Su alcune applicazioni di un tipo di convergenza variazionale, Ann. Scuola Norm. Sup. Pisa, 2 (1975), 617-638.
191. C. SBORDONE, Lower semicomtinuity and regularity of minima of variational integrals, in Nonlinear P.D.E and Appl., Collège de France Seminar, edited by H. Brézis and J. L. Lions, Pitman, 1983, 194-213.
192. J. SERRIN, On the definition and properties of certain variational integrals, Trans. Amer. Math. Soc., 101 (1961), 139-167.
193. J. SERRIN, Gradient estimates for solutions of nonlinear elliptic and parabolic equations, in Contributions to nonlinear functional analysis, edited by E. H. Zarantonello, Academic Press, San Diego, 1971, 565-601.
194. L. SIMON, Interior gradients bounds for non-uniformly elliptic equations, Indiana Univ. Math. J., 25 (1976), 821-855.
195. S. L. SOBOLEV, Ob odnoj teoreme funkcional'nogo analiza, Mat. Sb., 4 (1938), 471-497.
196. S. SPAGNOLO, Sulla convergenza di soluzioni di equazioni paraboliche ed ellittiche, Ann. Scuola Norm. Sup. Pisa, 22 (1968), 571-597.
197. G. STAMPACCHIA, Problemi al contorno ellittici, con dati discontinui, dotati di soluzioni hölderiane, Ann. Mat. Pura Appl., 51 (1960), 1-37
198. G. STAMPACCHIA, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier, 15 (1965), 189-258.
199. G. STAMPACCHIA, Equations elliptiques du second ordre à coefficients discontinus, Les Presses de l'Université de Montreal, 1966.
200. B. STROFFOLINI, Global boundedness of solutions of anisotropic variational problems, Boll. Un. Mat. Ital., 5-A (1991), 345-352.
201. A.I. SUBBOTIN, Generalized solutions of first order partial differential equations: the dynamical optimization perspective, Birkhauser, Boston, 1995.
202. V. ŠVERÁK, Rank-one convexity does not imply quasiconvexity, Proc. Roy. Soc. Edinburgh, 120A (1992), 185-189.
203. V. ŠVERÁK, On the problem of two wells, Geometric parametres and the relaxation of multiwell energies, in Microstructure and phase transition, edited by D. Kinderlehrer et al., Springer, 1992.
204. R. TAHRAOUI, Théorèmes d'existence en calcul des variations et applications à l'élasticité non linéaire, C. R. Acad. Sci. Paris, 302 (1986), 495-498. Also in Proc. Royal Soc. Edinburgh, 109A (1988), 51-78.
205. R. TAHRAOUI, Théorèmes d'existence en calcul des variations et applications à l'élasticité non linéaire, C. R. Acad. Sci. Paris, 302 (1986), 495- 498. Also in Proc. Royal Soc. Edinburgh, 109A (1988), 51-78.
206. R. TAHRAOUI, Sur une classe de fonctionnelles non convexes et applications, S.I.A.M. J. Math. Anal., 21 (1990), 37-52.
207. G. TALENTI, Calcolo delle variazioni, Quaderni dell'Unione Matematica Italiana n. 2, Pitagora Ed., 1977.
208. G. TALENTI, Boundedness of minimizers, Hokkaido Math. J., 19 (1990), 259-279.
209. TANG QI, Regularity of minimizers of nonisotropic integrals in the calculus of variations, Ann. Mat. Pura Appl., 164 (1993), 77-87.
210. L. TARTAR, Compensated compactness, Heriot-Watt Sympos. 4, Pitman, New York, 1978.
211. L. TARTAR, Estimations fines des coefficients homogénéisés, in Ennio De Giorgi Colloquium, edited by P. Krée, Research Notes in Math., no. 125, Pitman, London, 1985, 168-187.
212. F. TOMARELLI, A quasi-variational problem in nonlinear elasticity, Ann. Mat. Pura Appl., 158 (1991), 331-389.
213. L. TONELLI, Fondamenti di calcolo delle variazioni, Volume primo, Zanichelli, Bologna, 1921.
214. L. TONELLI, Fondamenti di calcolo delle variazioni, Volume secondo, Zanichelli, Bologna, 1923.
215. L. TONELLI, Il calcolo delle variazioni secondo la scuola, italiana e i suoi più recenti risultati, Atti del I Congresso UMI (Firenze, 1937), 26-1962, 419-435. 39. Ristampa in L. TONELLI, Opere scelte, Roma, Cremonese, Vol. III, 1962, 419-435.
216. L. TONELLI, Il calcolo delle variazioni secondo la scuola, italiana e i suoi più recenti risultati, Atti del I Congresso UMI (Firenze, 1937), 26- 1962, 419-435. 39. Ristampa in L. TONELLI, Opere scelte, Roma, Cremonese, Vol. III, 1962, 419-435.
217. P. TOLKSDORFF, Everywhere regularity for some quasilinear systems with a lack of ellipticity, Ann. Mat. Pura Appl., 134 (1983), 241-266.
218. N.S. TRUDINGER, On Harnack type inequalities and their application to quasilinear elliptic equations, Comm. Pure Appl. Math., 20 (1967), 721-747.
219. K. UHLENBECK, Regularity for a class of non-linear elliptic systems, Acta Math., 138 (1977), 219-240.
220. L. C. YOUNG, Lectures on the calculus of variations and optimal control theory, W. B. Saunders Company, Philadelphia, 1969.
221. V. V. ZHIKOV - S. M. KOZLOV - O. A. OLEINIK - KHA T'EN NGOAN, Averaging and G-convergence of differential operators, Uspeki Math. Nauk, 34 (1979), 65-133; Russian Math. Surveys, 34 (1979), 69-147.
222. V. V. ZHIKOV - S. M. KOZLOV - O. A. OLEINIK - KHA T'EN NGOAN, Averaging and G-convergence of differential operators, Uspeki Math. Nauk, 34 (1979), 65-133; Russian Math. Surveys, 34 (1979), 69-147.