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Volumn 230, Issue 2, 1999, Pages 259-316

A geometrical approach to monotone functions in ℝn

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EID: 0033482196     PISSN: 00255874     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00004691     Document Type: Article
Times cited : (141)

References (59)
  • 1
    • 84971972568 scopus 로고
    • Rank-one property for derivatives of functions with bounded variation
    • G. Alberti: Rank-one property for derivatives of functions with bounded variation, Proc. Royal Soc. Edinburgh 123-A (1993), 239-274.
    • (1993) Proc. Royal Soc. Edinburgh , vol.123 A , pp. 239-274
    • Alberti, G.1
  • 2
    • 0002967985 scopus 로고
    • On the structure of singular sets of convex functions
    • G. Alberti: On the structure of singular sets of convex functions, Calc. Var. 2 (1994), 17-27.
    • (1994) Calc. Var. , vol.2 , pp. 17-27
    • Alberti, G.1
  • 6
    • 84972551572 scopus 로고
    • Singularities and rank one properties of hessian measures
    • P. Aviles, Y. Giga: Singularities and rank one properties of hessian measures, Duke Math. J. 58 (1989), 441-467.
    • (1989) Duke Math. J. , vol.58 , pp. 441-467
    • Aviles, P.1    Giga, Y.2
  • 7
    • 84972535466 scopus 로고
    • Convex functions and upper semicontinuous functions
    • R.D. Anderson, V.L. Klee: Convex functions and upper semicontinuous functions, Duke Math. J. 19 (1952), 349-357.
    • (1952) Duke Math. J. , vol.19 , pp. 349-357
    • Anderson, R.D.1    Klee, V.L.2
  • 8
    • 0002867833 scopus 로고
    • Almost everywhere existence of the second differential of a convex function and some properties of convex surfaces connected with it
    • in Russian.
    • A.D. Aleksandrov: Almost everywhere existence of the second differential of a convex function and some properties of convex surfaces connected with it, Leningrad Univ. Ann. (Math, ser.) 6 (1939), 3-35 (in Russian).
    • (1939) Leningrad Univ. Ann. (Math, Ser.) , vol.6 , pp. 3-35
    • Aleksandrov, A.D.1
  • 9
    • 0001400376 scopus 로고
    • A compactness theorem for a special class of functions of bounded variation
    • L. Ambrosio: A compactness theorem for a special class of functions of bounded variation, Boll. Un. Mat. Ital. 3-B (1989), 857-881.
    • (1989) Boll. Un. Mat. Ital. , vol.3 B , pp. 857-881
    • Ambrosio, L.1
  • 10
    • 0000465804 scopus 로고
    • Existence theory for a new class of variational problems
    • L. Ambrosio: Existence theory for a new class of variational problems, Arch. Rat. Mech. and Anal. 111 (1990), 291-322.
    • (1990) Arch. Rat. Mech. and Anal. , vol.111 , pp. 291-322
    • Ambrosio, L.1
  • 11
    • 84936405686 scopus 로고
    • Su alcune proprietà delle funzioni convesse
    • L. Ambrosio: Su alcune proprietà delle funzioni convesse, Rend. Mat. Acc. Lincei (ser. IX) 3 (1992), 193-202.
    • (1992) Rend. Mat. Acc. Lincei (Ser. IX) , vol.3 , pp. 193-202
    • Ambrosio, L.1
  • 12
    • 0004392136 scopus 로고    scopus 로고
    • A note on the theory of S BV functions
    • G. Alberti, C. Mantegazza: A note on the theory of S BV functions, Boll. Un. Mat. It. (7), 11-B (1997), 375-382.
    • (1997) Boll. Un. Mat. It. , vol.11 B , Issue.7 , pp. 375-382
    • Alberti, G.1    Mantegazza, C.2
  • 13
    • 51249161652 scopus 로고
    • Singular sets of convex bodies and surfaces with generalized curvatures
    • G. Anzellotti, E. Ossanna: Singular sets of convex bodies and surfaces with generalized curvatures, Manuscripta Math. 86 (1995), 417-433.
    • (1995) Manuscripta Math. , vol.86 , pp. 417-433
    • Anzellotti, G.1    Ossanna, E.2
  • 14
    • 34250533132 scopus 로고
    • Frechét differentiability of convex functions
    • E. Asplund: Frechét differentiability of convex functions, Acta Math. 121 (1968), 31-48.
    • (1968) Acta Math. , vol.121 , pp. 31-48
    • Asplund, E.1
  • 15
    • 0003513119 scopus 로고
    • Variational convergence for functions and operators
    • Pitman, London
    • H. Attouch: Variational Convergence for Functions and Operators, Research Notes in Math., Pitman, London 1984.
    • (1984) Research Notes in Math.
    • Attouch, H.1
  • 16
    • 0017417265 scopus 로고
    • Convexity conditions and existence theorems in nonlinear elasticity
    • J.M. Ball: Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rat. Mech. and Anal. 63 (1977), 337-403.
    • (1977) Arch. Rat. Mech. and Anal. , vol.63 , pp. 337-403
    • Ball, J.M.1
  • 17
    • 0039314072 scopus 로고    scopus 로고
    • On the second differentiability of convex surfaces
    • G. Bianchi, A. Colesanti, C. Pucci: On the second differentiability of convex surfaces, Geom. Dedicata 60 (1996), 39-48.
    • (1996) Geom. Dedicata , vol.60 , pp. 39-48
    • Bianchi, G.1    Colesanti, A.2    Pucci, C.3
  • 18
    • 0041093444 scopus 로고
    • On singular points of convex surfaces
    • Am. Math. Soc., Providence
    • A.S. Besicovitch: On singular points of convex surfaces, in Proceedings of Symposia in Pure Mathematics VII, pp. 21-23, Am. Math. Soc., Providence 1963.
    • (1963) Proceedings of Symposia in Pure Mathematics , vol.7 , pp. 21-23
    • Besicovitch, A.S.1
  • 20
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • M.G. Crandall, H. Ishii, P.L. Lions: User's guide to viscosity solutions of second order partial differential equations, Bull. of the Amer. Math. Soc. 27 (1992), 1-67.
    • (1992) Bull. of the Amer. Math. Soc. , vol.27 , pp. 1-67
    • Crandall, M.G.1    Ishii, H.2    Lions, P.L.3
  • 22
    • 44049118235 scopus 로고
    • Multifractal decomposition of Moran fractals
    • R. Cawley, R.D. Mauldin: Multifractal decomposition of Moran fractals, Advances in Math. 92 (1992), 196-236.
    • (1992) Advances in Math. , vol.92 , pp. 196-236
    • Cawley, R.1    Mauldin, R.D.2
  • 23
    • 0003211244 scopus 로고
    • Convex analysis and measurable multifunctions
    • Springer-Verlag, Berlin
    • C. Castaing, M. Valadier: Convex Analysis and Measurable Multifunctions, Lect. Notes in Math. 580, Springer-Verlag, Berlin 1977.
    • (1977) Lect. Notes in Math. , vol.580
    • Castaing, C.1    Valadier, M.2
  • 24
    • 0007267558 scopus 로고
    • On the differentiability of functions which are of bounded variation in Tonelli's sense
    • A.P. Calderón, A. Zygmund: On the differentiability of functions which are of bounded variation in Tonelli's sense, Rev. Union Mat. Argentina 20 (1960), 102-121.
    • (1960) Rev. Union Mat. Argentina , vol.20 , pp. 102-121
    • Calderón, A.P.1    Zygmund, A.2
  • 25
    • 85067946483 scopus 로고
    • Direct methods in the calculus of variations
    • Springer-Verlag, New York
    • B. Dacorogna: Direct Methods in the Calculus of Variations, Applied Math. Sciences 78, Springer-Verlag, New York 1989.
    • (1989) Applied Math. Sciences , vol.78
    • Dacorogna, B.1
  • 27
    • 0000515079 scopus 로고
    • On second derivatives of convex functions
    • R.M. Dudley: On second derivatives of convex functions, Math. Scand. 41 (1977), 159-174.
    • (1977) Math. Scand. , vol.41 , pp. 159-174
    • Dudley, R.M.1
  • 32
    • 84968469617 scopus 로고
    • Curvature measures
    • H. Federer: Curvature measures, Trans. Am. Math. Soc. 93 (1959), 418-491.
    • (1959) Trans. Am. Math. Soc. , vol.93 , pp. 418-491
    • Federer, H.1
  • 34
    • 0002230428 scopus 로고
    • Cartesian currents, weak diffeomorphism, and existence theorems in nonlinear elasticity
    • Erratum and addendum, Arch. Rat. Mech. and Anal. 109 (1990), 385-392
    • M. Giaquinta, G. Modica, J. Souček: Cartesian currents, weak diffeomorphism, and existence theorems in nonlinear elasticity, Arch. Rat. Mech. and Anal. 106 (1989), 97-159. Erratum and addendum, Arch. Rat. Mech. and Anal. 109 (1990), 385-392.
    • (1989) Arch. Rat. Mech. and Anal. , vol.106 , pp. 97-159
    • Giaquinta, M.1    Modica, G.2    Souček, J.3
  • 35
    • 0000863430 scopus 로고
    • Graphs of finite mass which cannot be approximated in area by smooth graphs
    • M. Giaquinta, G. Modica, J. Souček: Graphs of finite mass which cannot be approximated in area by smooth graphs, Manuscr. Math. 78 (1993), 259-271.
    • (1993) Manuscr. Math. , vol.78 , pp. 259-271
    • Giaquinta, M.1    Modica, G.2    Souček, J.3
  • 37
    • 0040499318 scopus 로고
    • How well can space be packed with smooth bodies? Measure theoretic results
    • P.M. Gruber: How well can space be packed with smooth bodies? Measure theoretic results, J. London Math. Soc. 52 (1995), 1-14.
    • (1995) J. London Math. Soc. , vol.52 , pp. 1-14
    • Gruber, P.M.1
  • 38
    • 0001265433 scopus 로고
    • Fractals and self-similarity
    • J.E. Hutchinson: Fractals and self-similarity, Indiana Univ. Math. J. 30 (1981), 713-747.
    • (1981) Indiana Univ. Math. J. , vol.30 , pp. 713-747
    • Hutchinson, J.E.1
  • 39
    • 33845220501 scopus 로고
    • The Gibbs-Thompson relation within the gradient theory of phase transitions
    • S. Luckhaus, L. Modica: The Gibbs-Thompson relation within the gradient theory of phase transitions, Arch. Rat. Mech. and Anal. 107 (1989), 71-83.
    • (1989) Arch. Rat. Mech. and Anal. , vol.107 , pp. 71-83
    • Luckhaus, S.1    Modica, L.2
  • 40
    • 84972488065 scopus 로고
    • Monotone nonlinear operators on a Hilbert space
    • G. Minty: Monotone nonlinear operators on a Hilbert space, Duke Math. J. 29 (1962), 341-346.
    • (1962) Duke Math. J. , vol.29 , pp. 341-346
    • Minty, G.1
  • 41
    • 0001635734 scopus 로고
    • Contrôle optimal dans les inéquations variationelles elliptiques
    • F. Mignot: Contrôle optimal dans les inéquations variationelles elliptiques, J. Funct. Anal. 22 (1976), 130-185.
    • (1976) J. Funct. Anal. , vol.22 , pp. 130-185
    • Mignot, F.1
  • 43
    • 0001050313 scopus 로고
    • Weak continuity of determinants and nonlinear elasticity
    • S. Müller: Weak continuity of determinants and nonlinear elasticity, C.R. Acad. Sci. Paris, 307-I (1988), 501-506.
    • (1988) C.R. Acad. Sci. Paris , vol.307 I , pp. 501-506
    • Müller, S.1
  • 44
    • 0002154673 scopus 로고
    • Det = det. A remark on the distributional determinant
    • S. Müller: Det = det. A remark on the distributional determinant, C.R. Acad. Sci. Paris, 311-I (1990), 13-17.
    • (1990) C.R. Acad. Sci. Paris , vol.311 I , pp. 13-17
    • Müller, S.1
  • 45
    • 85012277782 scopus 로고
    • On the singular support of the distributional determinant
    • S. Müller: On the singular support of the distributional determinant, Ann. I.H.P. Analyse non linéaire 10 (1993), 657-696.
    • (1993) Ann. I.H.P. Analyse Non Linéaire , vol.10 , pp. 657-696
    • Müller, S.1
  • 46
    • 51249163499 scopus 로고
    • Approximation in area of graphs with isolated singularities
    • D. Mucci: Approximation in area of graphs with isolated singularities, Manuscripta Math. 88 (1995), 135-146.
    • (1995) Manuscripta Math. , vol.88 , pp. 135-146
    • Mucci, D.1
  • 48
    • 0003323056 scopus 로고
    • Convex functions, monotone operators and differentiability
    • Springer-Verlag, New York
    • R.R. Phelps: Convex Functions, Monotone Operators and Differentiability, Lect. Notes in Math. 1364, Springer-Verlag, New York 1989.
    • (1989) Lect. Notes in Math. , vol.1364
    • Phelps, R.R.1
  • 50
    • 84968505797 scopus 로고
    • Fréchet differentiation of convex functions in a Banach space with separable dual
    • D. Preiss, L. Zajíček: Fréchet differentiation of convex functions in a Banach space with separable dual, Proc. Amer. Math. Soc. 91 (1984), 202-204.
    • (1984) Proc. Amer. Math. Soc. , vol.91 , pp. 202-204
    • Preiss, D.1    Zajíček, L.2
  • 51
    • 0001503348 scopus 로고
    • Weak convergence of completely additive vector functions on a set
    • Yu.G. Reshetnyak: Weak convergence of completely additive vector functions on a set, Siberian Math. J. 9 (1968), 1039-1045.
    • (1968) Siberian Math. J. , vol.9 , pp. 1039-1045
    • Reshetnyak, Yu.G.1
  • 52
    • 0001060655 scopus 로고
    • Generalized derivatives and differentiability almost everywhere
    • Yu.G. Reshetnyak: Generalized derivatives and differentiability almost everywhere. Math. USSR Sb. 4 (1968), 293-302.
    • (1968) Math. USSR Sb. , vol.4 , pp. 293-302
    • Reshetnyak, Yu.G.1
  • 55
    • 0041093447 scopus 로고
    • On the multiplicity points of monotone operators on a separable banch spaces I and II, comment
    • L. Veselý: On the multiplicity points of monotone operators on a separable Banch spaces I and II, Comment. Math. Univ. Carolina; 27 (1986), 551-570, and 28 (1987), 295-299.
    • (1986) Math. Univ. Carolina , vol.27 , pp. 551-570
    • Veselý, L.1
  • 56
    • 33747188172 scopus 로고
    • L. Veselý: On the multiplicity points of monotone operators on a separable Banch spaces I and II, Comment. Math. Univ. Carolina; 27 (1986), 551-570, and 28 (1987), 295-299.
    • (1987) Math. Univ. Carolina , vol.28 , pp. 295-299
  • 57
    • 0001168879 scopus 로고
    • Spaces BV and quasi-linear equations
    • A.I. Vol'pert: Spaces BV and quasi-linear equations, Math. USSR Sb. 17 (1967), 225-267.
    • (1967) Math. USSR Sb. , vol.17 , pp. 225-267
    • Vol'pert, A.I.1
  • 58
    • 0001049856 scopus 로고
    • On the points of multiplicity of monotone operators, comment
    • L. Zajíček: On the points of multiplicity of monotone operators, Comment. Mat. Univ. Carolina: 19 (1978), 179-189.
    • (1978) Mat. Univ. Carolina , vol.19 , pp. 179-189
    • Zajíček, L.1
  • 59
    • 0000884525 scopus 로고
    • On the differentiability of convex functions in finite and infinite dimensional spaces
    • L. Zajíček: On the differentiability of convex functions in finite and infinite dimensional spaces, Czechoslovak Math. J. 29 (104) (1979), 340-348.
    • (1979) Czechoslovak Math. J. , vol.29 , Issue.104 , pp. 340-348
    • Zajíček, L.1


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