Implicit second order partial differential equations

 Access to full text

 Full (PDF)

1. [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. Zbl0459.35020MR615159
2. [2] J.M. Ball - R.D. James, Fine phase mixtures as minimizers of energy, Arch. Rational Mech. Anal.100 (1987), 15-52. Zbl0629.49020MR906132
3. [3] R. Bellman, "Introduction to matrix analysis", McGraw-Hill, New York, 1960. Zbl0124.01001MR122820
4. [4] A. Bressan - F. Flores, On total differential inclusions, Rend. Sem. Mat. Univ. Padova92 (1994), 9-16. Zbl0821.35158MR1320474
5. [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. Zbl0598.35047MR739925
6. [6] A. Cellina, On the differential inclusion, x' ∈ [-1, 1], Atti. Accad. Naz. Lincei, Rend. Sci. Fis. Mat. Nat.69 (1980), 1-6. Zbl0922.34009
7. [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. Zbl0755.35015MR1118699
8. [8] B. Dacorogna, "Direct methods in the calculus of variations", Applied Math. Sciences, 78, Springer, Berlin, 1989. Zbl0703.49001MR990890
9. [9] B. Dacorogna - P. Marcellini, Existence of minimizers for non quasiconvex integrals, Arch. Rational Mech. Anal.131 (1995), 359-399. Zbl0837.49002MR1354700
10. [10] B. Dacorogna - P. Marcellini, Théorème d'existence dans le cas scalaire et vectoriel pour les équations de Hamilton-Jacobi, C.R. Acad. Sci. Paris322 (1996), 237-240. Zbl0846.35028MR1378259
11. [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. Paris323 (1996), 599-602. Zbl0860.35020MR1411049
12. [12] B. Dacorogna - P. Marcellini, General existence theorems for Hamilton-Jacobi equations in the scalar and vectorial cases, Acta Mathematica, 178 (1997), 1-37. Zbl0901.49027MR1448710
13. [13] B. Dacorogna - P. Marcellini, Cauchy-Dirichlet problem for first order nonlinear systems, J. Functional Analysis, to appear. Zbl0911.35034MR1411049
14. [14] F.S. De Blasi - G. Pianigiani, A Baire category approach to the existence of solutions of multivalued differential equations in Banch spaces, Funkcialaj Ekvacioj25 (1982), 153-162. Zbl0535.34009MR694909
15. [15] F.S. De Blasi - G. Pianigiani, Non convex valued differential inclusions in Banach spaces, J. Math. Anal. Appl.157 (1991), 469-494. Zbl0728.34013MR1112329
16. [16] L.C. Evans, Classical solutions of fully nonlinear, convex, second-order elliptic equations, Comm. Pure Appl. Math.25 (1982), 333-363. Zbl0469.35022MR649348
17. [17] N. Fusco, Quasi-convessità e semicontinuità per integrali multipli di ordine superiore, Ricerche di Matematica29 (1980), 307-323. Zbl0508.49012
18. [18] M. Guidorzi - L. Poggiolini, Lower semicontinuity for quasiconvex integrals of higher order, preprint 1997. Zbl0930.35059MR1691445
19. [19] N.G. Meyers, Quasiconvexity and the semicontinuity of multiple integrals, Trans. Amer. Math. Soc.119 (1965), 125-149. Zbl0166.38501MR188838
20. [20] C.B. Morrey, "Multiple integrals in the calculus of variations", Springer, Berlin, 1966. Zbl0142.38701
21. [21] S. Müller - V. Sverak, "Attainment results for the two-well problem by convex integration ", edited by J. Jost, International Press1996, pp. 239-251. Zbl0930.35038MR1449410
22. [22] N.S. Trudinger, Fully nonlinear, uniformly elliptic equations under natural structure conditions, Trans. Amer. Math. Soc.278 (1983), 751-769. Zbl0518.35036MR701522

1. Kewei Zhang, On the quasiconvex exposed points
2. Kewei Zhang, On the quasiconvex exposed points
3. Bernard Dacorogna, A new approach to the existence of almost everywhere solutions of nonlinear PDEs