Implicit second order partial differential equations
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 25 (1997) no. 1-2, p. 299-328
@article{ASNSP_1997_4_25_1-2_299_0,
     author = {Dacorogna, Bernard and Marcellini, Paolo},
     title = {Implicit second order partial differential equations},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 25},
     number = {1-2},
     year = {1997},
     pages = {299-328},
     zbl = {1003.35043},
     mrnumber = {1655520},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1997_4_25_1-2_299_0}
}
Dacorogna, Bernard; Marcellini, Paolo. Implicit second order partial differential equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 25 (1997) no. 1-2, pp. 299-328. http://www.numdam.org/item/ASNSP_1997_4_25_1-2_299_0/

[1] J.M. Ball - J.C. Curie - P.J. Olver, Null Lagrangians, weak continuity and variational problems of arbitrary order, J. Funct. Anal. 41 (1981), 135-174. | MR 615159 | Zbl 0459.35020

[2] J.M. Ball - R.D. James, Fine phase mixtures as minimizers of energy, Arch. Rational Mech. Anal. 100 (1987), 15-52. | MR 906132 | Zbl 0629.49020

[3] R. Bellman, "Introduction to matrix analysis", McGraw-Hill, New York, 1960. | MR 122820 | Zbl 0124.01001

[4] A. Bressan - F. Flores, On total differential inclusions, Rend. Sem. Mat. Univ. Padova 92 (1994), 9-16. | Numdam | MR 1320474 | Zbl 0821.35158

[5] L. Caffarelli - L. Nirenberg - J. Spruck, The Dirichlet problem for nonlinear second order elliptic equations, I: Monge-Ampère equations, Comm. Pure Appl. Math. 37 (1984), 369-402. | MR 739925 | Zbl 0598.35047

[6] A. Cellina, On the differential inclusion, x' ∈ [-1, 1], Atti. Accad. Naz. Lincei, Rend. Sci. Fis. Mat. Nat. 69 (1980), 1-6. | Zbl 0922.34009

[7] 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. | MR 1118699 | Zbl 0755.35015

[8] B. Dacorogna, "Direct methods in the calculus of variations", Applied Math. Sciences, 78, Springer, Berlin, 1989. | MR 990890 | Zbl 0703.49001

[9] B. Dacorogna - P. Marcellini, Existence of minimizers for non quasiconvex integrals, Arch. Rational Mech. Anal. 131 (1995), 359-399. | MR 1354700 | Zbl 0837.49002

[10] B. Dacorogna - P. Marcellini, Théorème d'existence dans le cas scalaire et vectoriel pour les équations de Hamilton-Jacobi, C.R. Acad. Sci. Paris 322 (1996), 237-240. | MR 1378259 | Zbl 0846.35028

[11] 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. | MR 1411049 | Zbl 0860.35020

[12] B. Dacorogna - P. Marcellini, General existence theorems for Hamilton-Jacobi equations in the scalar and vectorial cases, Acta Mathematica, 178 (1997), 1-37. | MR 1448710 | Zbl 0901.49027

[13] B. Dacorogna - P. Marcellini, Cauchy-Dirichlet problem for first order nonlinear systems, J. Functional Analysis, to appear. | MR 1411049 | Zbl 0911.35034

[14] 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. | MR 694909 | Zbl 0535.34009

[15] F.S. De Blasi - G. Pianigiani, Non convex valued differential inclusions in Banach spaces, J. Math. Anal. Appl. 157 (1991), 469-494. | MR 1112329 | Zbl 0728.34013

[16] L.C. Evans, Classical solutions of fully nonlinear, convex, second-order elliptic equations, Comm. Pure Appl. Math. 25 (1982), 333-363. | MR 649348 | Zbl 0469.35022

[17] N. Fusco, Quasi-convessità e semicontinuità per integrali multipli di ordine superiore, Ricerche di Matematica 29 (1980), 307-323. | Zbl 0508.49012

[18] M. Guidorzi - L. Poggiolini, Lower semicontinuity for quasiconvex integrals of higher order, preprint 1997. | MR 1691445

[19] N.G. Meyers, Quasiconvexity and the semicontinuity of multiple integrals, Trans. Amer. Math. Soc. 119 (1965), 125-149. | MR 188838 | Zbl 0166.38501

[20] C.B. Morrey, "Multiple integrals in the calculus of variations", Springer, Berlin, 1966. | Zbl 0142.38701

[21] S. Müller - V. Sverak, "Attainment results for the two-well problem by convex integration ", edited by J. Jost, International Press 1996, pp. 239-251. | MR 1449410 | Zbl 0930.35038

[22] N.S. Trudinger, Fully nonlinear, uniformly elliptic equations under natural structure conditions, Trans. Amer. Math. Soc. 278 (1983), 751-769. | MR 701522 | Zbl 0518.35036