Existence of minimizers and lower semicontinuity of integral functionals in the vectorial case
Rendiconti del Seminario Matematico della Università di Padova, Tome 102 (1999), pp. 125-140. 
@article{RSMUP_1999__102__125_0,
     author = {Bertirotti, Silvia and Van der Putten, Roberto},
     title = {Existence of minimizers and lower semicontinuity of integral functionals in the vectorial case},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {125--140},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {102},
     year = {1999},
     mrnumber = {1739536},
     zbl = {0945.49008},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_1999__102__125_0/}
}
TY  - JOUR
AU  - Bertirotti, Silvia
AU  - Van der Putten, Roberto
TI  - Existence of minimizers and lower semicontinuity of integral functionals in the vectorial case
JO  - Rendiconti del Seminario Matematico della Università di Padova
PY  - 1999
SP  - 125
EP  - 140
VL  - 102
PB  - Seminario Matematico of the University of Padua
UR  - http://www.numdam.org/item/RSMUP_1999__102__125_0/
LA  - en
ID  - RSMUP_1999__102__125_0
ER  - 
%0 Journal Article
%A Bertirotti, Silvia
%A Van der Putten, Roberto
%T Existence of minimizers and lower semicontinuity of integral functionals in the vectorial case
%J Rendiconti del Seminario Matematico della Università di Padova
%D 1999
%P 125-140
%V 102
%I Seminario Matematico of the University of Padua
%U http://www.numdam.org/item/RSMUP_1999__102__125_0/
%G en
%F RSMUP_1999__102__125_0
Bertirotti, Silvia; Van der Putten, Roberto. Existence of minimizers and lower semicontinuity of integral functionals in the vectorial case. Rendiconti del Seminario Matematico della Università di Padova, Tome 102 (1999), pp. 125-140. http://www.numdam.org/item/RSMUP_1999__102__125_0/

[A] L. Ambrosio, New lower semicontinuity results for integral functional, Rend. Accad. Naz. Sci. XL Mem. Sci. Mat. Fis. Natur. (5), 11 (1987), pp. 1-42. | MR | Zbl

[B] J.M. Ball, Global invertibility of Sobolev functions and the inter-penetration of matter, Proc. Royal Soc. Edinburgh, 88A (1981), pp. 315-328. | MR | Zbl

[Br] Y. Brenier, Polar factorization and monotone rearrangement of vector-valued functions, Comm. Pure Appl. Math., XLIV (1991), pp. 375-417. | MR | Zbl

[C1] L.A. Caffarelli, The regularity of mappings with a convex potential, J.A.M.S., 5 (1992), pp. 99-104. | MR | Zbl

[C2] L.A. Caffarelli, Boundary regularity of maps with convex potential-II, Annals of Mathematics, 144 (1996), pp. 453-496. | MR | Zbl

[D] B. Dacorogna, A relaxation theorem and its applications to the equilibrium of gases, Arch. Ration. Mech. Anal., 77 (1981), pp. 359-386. | MR | Zbl

[DMa] B. Dacorogna - P. Marcellini, General existence theorems for Hamilton-Jacobi equations in the scalar and vectorial cases, Acta Math., 178 (1997), pp. 1-37. | MR | Zbl

[DMo] B. Dacorogna - J. Moser, On a Partial Differential Equation involving the Jacobian determinant, Ann. Inst. H. Poincaré Anal. Non Linéaire, 7 (1990), pp. 1-26. | Numdam | MR | Zbl

[DGBDM] E. De Giorgi - G. Buttazzo - G. Dal Maso, On the lower semicontinuity of certain integral functional, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8), 74 (1983), pp. 274-282. | MR | Zbl

[ET] I. Ekeland - R. Teman, Convex analysis and variational problems, North Holland, Amsterdam (1978). | Zbl

[FT] I. Fonseca - L. Tartar, The displacement problem for elastic crystal, Proceedings of the Royal Society of Edinburgh, 113A (1989), pp. 159-180. | MR | Zbl

[G] W. Gangbo, An Elementary Proof of the Polar factorization of Vector-Valued Functions, Arch. Rational Mech. Anal., 128 (1994), pp. 381-399. | MR | Zbl

[GT] D. Gilbarg - N. Trudinger, Elliptic Partial Differential Equations of Second Order (second edition), Springer-Verlag-New York (1983). | MR | Zbl

[RR] T. Radó - P.V. Reichelderfer, Continuous transformations in analysis, Springer-Verlag-New York (1955). | MR

[R] Yu G. Reshetnyak, Space mappings with bounded distortion, Transl. Math. Monographs, 73, Amer. Math. Soc., Providence, RI (1989). | MR | Zbl

[V] R. Van Der Putten, Continuità e semicontinuità inferiore di funzionali integrali con integrande policonvesse, Boll. Un. Mat. Ital. (7), 6-B (1994), pp. 557-582. | MR | Zbl

[Z] S. Zagatti, On the Dirichlet Problem for Vectorial Hamilton-Jacoby Equations, Preprint SISSA 182/96/M (1997) | MR | Zbl