Unilateral problems for elliptic systems with gradient constraints

 Access to full text

 Full (PDF)

1. [1] A. A. Arkhipova, Regularity of the solution of a system of variational inequalities with constraint in ${ℝ}^N$, Vestnik Leningrad. Univ. 1984 (13), 5-9 (in Russian). 
2. [2] A. A. Arkhipova, Regularity of the problem with an obstacle up to the boundary for strongly elliptic operators, in: Some Applications of Functional Analysis to Problems of Mathematical Physics, Inst. Math., Siberian Branch of Acad. Sci. USSR, Novosibirsk 1988, 3-20 (in Russian). 
3. [3] A. A. Arkhipova, Minimal supersolutions for the obstacle problem, Izv. Akad. Nauk SSSR 37 (1973), 1156-1185 (in Russian). 
4. [4] A. A. Arkhipova and N. N. Ural'tseva, The regularity of solutions of variational inequalities under convex boundary constraints for a class of non-linear operators, Vestnik Leningrad. Univ. 1987 (15), 13-19 (in Russian). 
5. [5] L. Caffarelli, Further regularity for the Signorini problem, Comm. Partial Differential Equations 4 (1979), 1067-1075. Zbl0427.35019
6. [6] L. C. Evans, A second order elliptic equation with gradient constraint, ibid. 4 (1979), 555-572 and 1199. Zbl0448.35036
7. [7] A. Friedman, Variational Principles and Free-Boundary Problems, Wiley, New York 1982. Zbl0564.49002
8. [8] S. Hildebrandt and K.-O. Widman, Variational inequalities for vector-valued functions, J. Reine Angew. Math. 309 (1979), 191-220. Zbl0408.49012
9. [9] H. Ishii and S. Koike, Boundary regularity and uniqueness for an elliptic equation with gradient constraint, Comm. Partial Differential Equations 8 (1983), 317-346. Zbl0538.35012
10. [10] R. Jensen, Regularity for elastic-plastic type variational inequalities, Indiana Univ. Math. J. 32 (1983), 407-423. Zbl0554.35052
11. [11] D. Kinderlehrer, The smoothness of the solution of the boundary obstacle problem, J. Math. Pures Appl. 60 (1981), 193-212. Zbl0459.35092
12. [12] D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications, Acad. Press, New York 1980. Zbl0457.35001
13. [13] O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations, Nauka, Moscow 1973 (in Russian). 
14. [14] H. Lewy and G. Stampacchia, On the regularity of the solution of a variational inequality, Comm. Pure Appl. Math. 22 (1969), 153-188. Zbl0167.11501
15. [15] J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris 1969. Zbl0189.40603
16. [16] T. N. Rozhkovskaya, Unilateral problems with convex constraints on the gradient, in: Partial Differential Equations, Proc. S. L. Sobolev Seminar, Novosibirsk 1981, 78-85 (in Russian). 
17. [17] T. N. Rozhkovskaya, The smoothness of the solutions of the variational inequalities with gradient constraints, in: The Imbedding Theorems and Their Applications, Proc. S. L. Sobolev Seminar, Novosibirsk 1982, 128-138 (in Russian). 
18. [18] T. N. Rozhkovskaya, On one-sided problems for non-linear operators with convex constraints on the gradient of the solution, Dokl. Akad. Nauk SSSR 268 (1983), 38-41 (in Russian). English transl. in Soviet Math. Dokl. 27 (1983). Zbl0536.35027
19. [19] T. N. Rozhkovskaya, The regularity theorem for a unilateral problem with the convex constraints on the gradient of the solution, in: Problemy Mat. Anal. 9, Izdat. Leningrad. Univ., Leningrad 1984, 166-171; English transl. in J. Soviet Math. 35 (1) (1986). Zbl0643.35031
20. [20] T. N. Rozhkovskaya, Unilateral problems for elliptic operators with convex constraints on the gradient of the solution, Sibirsk. Mat. Zh. 26 (3) (1985), 134-146 and 26 (5) (1985), 150-158 (in Russian). Zbl0598.35049
21. [21] T. N. Rozhkovskaya, One-sided problems for parabolic quasilinear operators, Dokl. Akad. Nauk SSSR 290 (3) (1986), 549-552 (in Russian). 
22. [22] T. N. Rozhkovskaya, Unilateral problems with convex constraints for quasilinear parabolic operators, Sibirsk. Mat. Zh. 29 (5) (1988), 198-211 (in Russian). Zbl0677.35060
23. [23] G. M. Troianiello, Maximal and minimal solutions to a class of elliptic quasilinear problems, Proc. Amer. Math. Soc. 91 (1) (1984), 95-101. Zbl0524.35051
24. [24] N. N. Ural'tseva, Hölder continuity of gradients of solutions of parabolic equations under the Signorini conditions on the boundary, Dokl. Akad. Nauk SSSR 280 (3) (1985), 563-565 (in Russian). 
25. [25] N. N. Ural'tseva, On the regularity of solutions of variational inequalities, Uspekhi Mat. Nauk 42 (6) (1987), 151-174 (in Russian). 
26. [26] M. Wiegner, The $C^{1,1}$-character of solutions of second order elliptic equations with gradient constraint, Comm. Partial Differential Equations 6 (1981), 361-371. Zbl0458.35035
27. [27] G. H. Williams, Nonlinear nonhomogeneous elliptic variational inequalities with a nonconstant gradient constraint, J. Math. Pures Appl. 60 (2) (1981), 213-226. Zbl0467.49005