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ArticleOriginal scientific text

Title

Unilateral problems for elliptic systems with gradient constraints

Authors 1

Affiliations

  1. Institute of Mathematics, Russian Academy of Sciences, Siberian Branch, Universitetskiĭ Prosp. 4, 630090 Novosibirsk, Russia

Bibliography

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  3. A. A. Arkhipova, Minimal supersolutions for the obstacle problem, Izv. Akad. Nauk SSSR 37 (1973), 1156-1185 (in Russian).
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  5. L. Caffarelli, Further regularity for the Signorini problem, Comm. Partial Differential Equations 4 (1979), 1067-1075.
  6. L. C. Evans, A second order elliptic equation with gradient constraint, ibid. 4 (1979), 555-572 and 1199.
  7. A. Friedman, Variational Principles and Free-Boundary Problems, Wiley, New York 1982.
  8. S. Hildebrandt and K.-O. Widman, Variational inequalities for vector-valued functions, J. Reine Angew. Math. 309 (1979), 191-220.
  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.
  10. R. Jensen, Regularity for elastic-plastic type variational inequalities, Indiana Univ. Math. J. 32 (1983), 407-423.
  11. D. Kinderlehrer, The smoothness of the solution of the boundary obstacle problem, J. Math. Pures Appl. 60 (1981), 193-212.
  12. D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications, Acad. Press, New York 1980.
  13. O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations, Nauka, Moscow 1973 (in Russian).
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  15. J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris 1969.
  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. 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. 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).
  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).
  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).
  21. T. N. Rozhkovskaya, One-sided problems for parabolic quasilinear operators, Dokl. Akad. Nauk SSSR 290 (3) (1986), 549-552 (in Russian).
  22. T. N. Rozhkovskaya, Unilateral problems with convex constraints for quasilinear parabolic operators, Sibirsk. Mat. Zh. 29 (5) (1988), 198-211 (in Russian).
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  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).
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Banach Center Publications
1992/27/2
Export to PBN, Opens in new tab
Pages:
425-445
Main language of publication
English
Published
1992
Exact and natural sciences