메뉴 건너뛰기




Volumn 20, Issue 3, 2004, Pages 301-328

A sharp attainment result for nonconvex variational problems

Author keywords

Convex integration; Existence of minimizers; Nonconvex variational problems

Indexed keywords


EID: 3042664415     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00526-003-0238-5     Document Type: Article
Times cited : (15)

References (40)
  • 1
    • 34249955899 scopus 로고
    • A non convex variational problem related to change of phase
    • Bauman, P., Phillips, D.: A non convex variational problem related to change of phase. Appl. Math. Optim. 21, 113-138 (1990)
    • (1990) Appl. Math. Optim. , vol.21 , pp. 113-138
    • Bauman, P.1    Phillips, D.2
  • 2
    • 0042044425 scopus 로고    scopus 로고
    • Existence and regularity of minimizers of non convex functional depending on u and ∇u
    • Celada, P.: Existence and regularity of minimizers of non convex functional depending on u and ∇u. J. Math. Anal. Appl. 230, 30-56 (1999)
    • (1999) J. Math. Anal. Appl. , vol.230 , pp. 30-56
    • Celada, P.1
  • 3
    • 0032443214 scopus 로고    scopus 로고
    • Existence and non existence of solutions to a variational problem on a square
    • Celada, P., Cellina, A.: Existence and non existence of solutions to a variational problem on a square. Houston J. Math. 24, 345-375 (1998)
    • (1998) Houston J. Math. , vol.24 , pp. 345-375
    • Celada, P.1    Cellina, A.2
  • 4
    • 23044520958 scopus 로고    scopus 로고
    • Minimizing non convex, multiple integrals: A density result
    • Celada, P., Perrotta, S.: Minimizing non convex, multiple integrals: a density result. Proc. Roy. Soc. Edinburgh 130A, 721-741 (2000)
    • (2000) Proc. Roy. Soc. Edinburgh , vol.130 A , pp. 721-741
    • Celada, P.1    Perrotta, S.2
  • 5
    • 0035917080 scopus 로고    scopus 로고
    • Minimizing nonconvex, simple integrals of product type
    • Celada, P., Perrotta, S.: Minimizing nonconvex, simple integrals of product type. J. Differential Equations 171, 148-172 (2001)
    • (2001) J. Differential Equations , vol.171 , pp. 148-172
    • Celada, P.1    Perrotta, S.2
  • 6
    • 0347036822 scopus 로고    scopus 로고
    • On the minimum problem for nonconvex, multiple integrals of product type
    • Celada, P., Perrotta, S.: On the minimum problem for nonconvex, multiple integrals of product type. Calc. Var. Partial Differential Equations 12, 371-398 (2001)
    • (2001) Calc. Var. Partial Differential Equations , vol.12 , pp. 371-398
    • Celada, P.1    Perrotta, S.2
  • 7
    • 0041425267 scopus 로고    scopus 로고
    • Existence of minimizers for nonconvex, noncoercive simple integrals
    • Celada, P., Perrotta, S.: Existence of minimizers for nonconvex, noncoercive simple integrals. SIAM J. Control Optim. 41, 1118-1140 (2002)
    • (2002) SIAM J. Control Optim. , vol.41 , pp. 1118-1140
    • Celada, P.1    Perrotta, S.2
  • 8
    • 0032222402 scopus 로고    scopus 로고
    • Existence of solutions for a class of non convex minimum problems
    • Celada, P., Perrotta, S., Treu, G.: Existence of solutions for a class of non convex minimum problems. Math. Z. 228, 177-199 (1998)
    • (1998) Math. Z. , vol.228 , pp. 177-199
    • Celada, P.1    Perrotta, S.2    Treu, G.3
  • 9
    • 38249004838 scopus 로고
    • On minima of a functional of the gradient: Necessary conditions
    • Cellina, A.: On minima of a functional of the gradient: necessary conditions. Nonlinear Anal. 20, 337-341 (1993)
    • (1993) Nonlinear Anal. , vol.20 , pp. 337-341
    • Cellina, A.1
  • 10
    • 38249005312 scopus 로고
    • On minima of a functional of the gradient: Sufficient conditions
    • Cellina, A.: On minima of a functional of the gradient: sufficient conditions. Nonlinear Anal. 20, 343-347 (1993)
    • (1993) Nonlinear Anal. , vol.20 , pp. 343-347
    • Cellina, A.1
  • 12
    • 0000780871 scopus 로고
    • On minima of radially symmetric functional of the gradient
    • Cellina, A., Perrotta, S.: On minima of radially symmetric functional of the gradient. Nonlinear Anal. 23 239-249 (1994)
    • (1994) Nonlinear Anal. , vol.23 , pp. 239-249
    • Cellina, A.1    Perrotta, S.2
  • 13
    • 85067946483 scopus 로고
    • Direct methods in the calculus of variations
    • Springer, Berlin
    • Dacorogna, B.: Direct methods in the Calculus of Variations. Number 78 in Appl. Math. Sci. Springer, Berlin 1989
    • (1989) Appl. Math. Sci. , vol.78
    • Dacorogna, B.1
  • 15
    • 0011216933 scopus 로고    scopus 로고
    • On the Dirichlet problem for Hamilton-Jacobi equations. A Baire category approach
    • De Blasi, F.S., Pianigiani, G.: On the Dirichlet problem for Hamilton-Jacobi equations. A Baire category approach. NoDEA Nonlinear Differential Equations Appl. 6, 13-34 (1999)
    • (1999) NoDEA Nonlinear Differential Equations Appl. , vol.6 , pp. 13-34
    • De Blasi, F.S.1    Pianigiani, G.2
  • 17
    • 0036410695 scopus 로고    scopus 로고
    • An existence result for a nonconvex variational problem via regularity
    • Fonseca, I., Fusco, N., Marcellini, P.: An existence result for a nonconvex variational problem via regularity. ESAIM Control Optim. Calc. Var. 7, 69-95 (2002)
    • (2002) ESAIM Control Optim. Calc. Var. , vol.7 , pp. 69-95
    • Fonseca, I.1    Fusco, N.2    Marcellini, P.3
  • 18
    • 0020881931 scopus 로고
    • Helical shear of an elastic, circular tube with a nonconvex stored energy
    • Fosdick, R.L., MacSithigh, G.: Helical shear of an elastic, circular tube with a nonconvex stored energy. Arch. Rational Mech. Anal. 84, 31-53 (1983)
    • (1983) Arch. Rational Mech. Anal. , vol.84 , pp. 31-53
    • Fosdick, R.L.1    MacSithigh, G.2
  • 19
    • 84973960437 scopus 로고
    • A necessary and sufficient condition for nonattainment and formation of microstructure almost everywhere in scalar variational problems
    • Friesecke, G.: A necessary and sufficient condition for nonattainment and formation of microstructure almost everywhere in scalar variational problems. Proc. Roy. Soc. Edinburgh Sect. A 124, 437-471 (1994)
    • (1994) Proc. Roy. Soc. Edinburgh Sect. A , vol.124 , pp. 437-471
    • Friesecke, G.1
  • 20
    • 0000602302 scopus 로고    scopus 로고
    • Existence of minimizers for some non convex one dimensional integrals
    • Fusco, N., Marcellini, P., Ornelas, A.: Existence of minimizers for some non convex one dimensional integrals. Portugal. Math. 55, 167-185 (1998)
    • (1998) Portugal. Math. , vol.55 , pp. 167-185
    • Fusco, N.1    Marcellini, P.2    Ornelas, A.3
  • 21
    • 0042154600 scopus 로고
    • Minima of some nonconvex, noncoercive problems
    • Giachetti, D., Schianchi, R.: Minima of some nonconvex, noncoercive problems. Ann. Mat. Pura Appl. 165 (4), 109-120 (1993)
    • (1993) Ann. Mat. Pura Appl. , vol.165 , Issue.4 , pp. 109-120
    • Giachetti, D.1    Schianchi, R.2
  • 22
    • 0001812542 scopus 로고
    • On the regularity of the minima of variational integrals
    • Giaquinta, M., Giusti, E.: On the regularity of the minima of variational integrals. Acta Math. 148, 31-46 (1982)
    • (1982) Acta Math. , vol.148 , pp. 31-46
    • Giaquinta, M.1    Giusti, E.2
  • 23
    • 0022766604 scopus 로고
    • Numerical study of a relaxed variational problem from optimal design
    • Goodman, J., Kohn, R.V., Reyna, L.: Numerical study of a relaxed variational problem from optimal design. Comput. Methods Appl. Mech. Engrg. 57, 107-127 (1986)
    • (1986) Comput. Methods Appl. Mech. Engrg. , vol.57 , pp. 107-127
    • Goodman, J.1    Kohn, R.V.2    Reyna, L.3
  • 24
    • 0003358469 scopus 로고
    • Partial differential relations
    • Springer, Berlin
    • Gromov, M.: Partial differential relations. Number 9 in Ergeb. Math. Grenzgeb. (3). Springer, Berlin 1986
    • (1986) Ergeb. Math. Grenzgeb. (3) , vol.9
    • Gromov, M.1
  • 25
    • 0000439529 scopus 로고
    • Analysis and numerical studies of a problem of shape design
    • Kawhol, B., Stara, J., Wittum, G.: Analysis and numerical studies of a problem of shape design. Arch. Rational Mech. Anal. 114, 349-363 (1991)
    • (1991) Arch. Rational Mech. Anal. , vol.114 , pp. 349-363
    • Kawhol, B.1    Stara, J.2    Wittum, G.3
  • 26
    • 84987788617 scopus 로고
    • A relation between existence of minima for non convex integrals and uniqueness for non strictly convex integrals of the calculus of variations
    • Cecconi, J.P., Zolezzi, T. (eds.) Mathematical theories of optimization, S. Margherita Ligure, Springer, Berlin
    • Marcellini, P.: A relation between existence of minima for non convex integrals and uniqueness for non strictly convex integrals of the Calculus of Variations. In: Cecconi, J.P., Zolezzi, T. (eds.) in Mathematical theories of optimization, number 979 in Lecture Notes in Math., pp. 216-231, S. Margherita Ligure (1981), Springer, Berlin 1983
    • (1981) Lecture Notes in Math. , vol.979 , pp. 216-231
    • Marcellini, P.1
  • 27
    • 84924362904 scopus 로고
    • Non convex integrals of the calculus of variations
    • Cellina, A. (ed.) in Methods of non convex analysis. Varenna. Springer, Berlin
    • Marcellini, P.: Non convex integrals of the Calculus of Variations. In: Cellina, A. (ed.) in Methods of non convex analysis, number 1446 in Lecture Notes in Math., pp. 16-57. Varenna (1989). Springer, Berlin 1990
    • (1989) Lecture Notes in Math. , vol.1446 , pp. 16-57
    • Marcellini, P.1
  • 28
    • 0011188010 scopus 로고
    • Non convex problems of the calculus of variations
    • Mascolo, E., Schianchi, R.: Non convex problems of the Calculus of Variations. Nonlinear Anal. 9, 371-379 (1985)
    • (1985) Nonlinear Anal. , vol.9 , pp. 371-379
    • Mascolo, E.1    Schianchi, R.2
  • 29
    • 38249034964 scopus 로고
    • Existence theorems in the calculus of variations
    • Mascolo, E., Schianchi, R.: Existence theorems in the Calculus of Variations. J. Differential Equations 67, 185-198 (1987)
    • (1987) J. Differential Equations , vol.67 , pp. 185-198
    • Mascolo, E.1    Schianchi, R.2
  • 30
    • 0001309171 scopus 로고    scopus 로고
    • Attainment results for the two-well problem by convex integration
    • Jost, J. (ed.). International Press, Cambridge, MA
    • Müller, S., Šverák, V.: Attainment results for the two-well problem by convex integration. In: Jost, J. (ed.) Geometric analysis and the calculus of variations, pp. 239-251. International Press, Cambridge, MA 1996
    • (1996) Geometric Analysis and the Calculus of Variations , pp. 239-251
    • Müller, S.1    Šverák, V.2
  • 31
    • 0000369212 scopus 로고    scopus 로고
    • Convex integration with constraints and applications to phase transitions and partial differential equations
    • Müller, S., Šverák, V.: Convex integration with constraints and applications to phase transitions and partial differential equations. J. Eur. Math. Soc. (JEMS) 1, 393-422 (1999)
    • (1999) J. Eur. Math. Soc. (JEMS) , vol.1 , pp. 393-422
    • Müller, S.1    Šverák, V.2
  • 32
    • 0012940979 scopus 로고    scopus 로고
    • Optimal existence theorems for nonhomogeneous differential inclusions
    • Müller, S., Sychev, M.A.: Optimal existence theorems for nonhomogeneous differential inclusions. J. Funct. Anal. 181, 447-475 (2001)
    • (2001) J. Funct. Anal. , vol.181 , pp. 447-475
    • Müller, S.1    Sychev, M.A.2
  • 33
    • 0001496391 scopus 로고
    • Calcul des variations et homogénéization
    • Bergman, D., et al. (eds.) in Les methodes de l'homogénéization: thèorie et applications en physique. Bréau sans Nappe. Eyrolles, Paris
    • Murat, F., Tartar, L.: Calcul des variations et homogénéization. In: Bergman, D., et al. (eds.) in Les methodes de l'homogénéization: thèorie et applications en physique, number 57 in Collect. Dir. Études Rech. Élec. France, pp. 316-369. Bréau sans Nappe (1983). Eyrolles, Paris 1985
    • (1983) Collect. Dir. Études Rech. Élec. France , vol.57 , pp. 316-369
    • Murat, F.1    Tartar, L.2
  • 34
    • 0011207047 scopus 로고
    • Existence of minimizers for vector problems without quasiconvexity condition
    • Raymond, J.P.: Existence of minimizers for vector problems without quasiconvexity condition. Nonlinear Anal. 18, 815-825 (1992)
    • (1992) Nonlinear Anal. , vol.18 , pp. 815-825
    • Raymond, J.P.1
  • 35
    • 0028496919 scopus 로고
    • Existence and uniqueness results for minimization problems with nonconvex functionals
    • Raymond, J.P.: Existence and uniqueness results for minimization problems with nonconvex functionals. J. Opt. Theory Appl. 82, 571-591 (1994)
    • (1994) J. Opt. Theory Appl. , vol.82 , pp. 571-591
    • Raymond, J.P.1
  • 36
    • 0010878597 scopus 로고
    • Theory of the integral
    • Hafner Publishing Co., G.E. Stechen, New York
    • Saks, S.: Theory of the integral. Number 7 in Monografie Matematyczne. Hafner Publishing Co., G.E. Stechen, New York 1937
    • (1937) Monografie Matematyczne , vol.7
    • Saks, S.1
  • 37
    • 23044520440 scopus 로고    scopus 로고
    • Characterization of homogeneous scalar variational problems solvable for all boundary data
    • Sychev, M.A.: Characterization of homogeneous scalar variational problems solvable for all boundary data. Proc. Roy. Soc. Edinburgh Sect. A 130, 611-631 (2000)
    • (2000) Proc. Roy. Soc. Edinburgh Sect. A , vol.130 , pp. 611-631
    • Sychev, M.A.1
  • 38
    • 0032398499 scopus 로고    scopus 로고
    • An existence result for a class of non convex problems of the calculus of variations
    • Treu, G.: An existence result for a class of non convex problems of the Calculus of Variations. J. Convex Anal. 5, 31-44 (1998)
    • (1998) J. Convex Anal. , vol.5 , pp. 31-44
    • Treu, G.1
  • 40
    • 0033902409 scopus 로고    scopus 로고
    • Minimization of functionals of the gradient by Baire's theorem
    • Zagatti, S.: Minimization of functionals of the gradient by Baire's theorem. SIAM J. Control Optim. 38, 384-399 (2000)
    • (2000) SIAM J. Control Optim. , vol.38 , pp. 384-399
    • Zagatti, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.