×

zbMATH — the first resource for mathematics

One-sided problems for elliptic operators with convex constraints on the gradient of the solution. II. (English. Russian original) Zbl 0598.35049
Sib. Math. J. 26, 750-757 (1985); translation from Sib. Mat. Zh. 26, No. 5(153), 150-158 (1985).
[For Part I, see ibid. 26, 414-424 (1985); translation from Sib. Mat. Zh. 26, No.3(151), 134-146 (1985; Zbl 0587.35040).]
This is a continuation of Part I. The existence theorem discussed in the first part is complemented here by results concerning the smoothness and uniqueness of the solution.
Reviewer: C.Constanda

MSC:
35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000)
35B65 Smoothness and regularity of solutions to PDEs
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] T. N. Rozhkovskaya, ?One-sided problems for elliptic operators with convex constraints on the gradient of the solution. I?, Sib. Mat. Zh.,26, No. 5, 134-146 (1985). · Zbl 0587.35040
[2] O. A. Ladyzhenskaya and N. N. Ural’tseva, Linear and Quasilinear Elliptic Equations, Academic Press, New York (1968).
[3] T. N. Rozhkovskaya, ?On unilateral problems with convex constraints on the gradient?, in: Partial Differential Equations, Trudy Sem. S. L. Soboleva, No. 2 (1981), pp. 78-85. · Zbl 0509.35041
[4] L. C. Evans, ?A second-order elliptic equation with gradient constraint?, Commun. Partial Diff. Equations?,4, No. 5, 555-572 (1979). · Zbl 0448.35036 · doi:10.1080/03605307908820103
[5] M. Wiegner, ?The C1,1-character of solutions of second-order elliptic equations with gradient constraint?, Commun. Partial Diff. Equations,6, No. 3, 361-371 (1981). · Zbl 0458.35035 · doi:10.1080/03605308108820181
[6] J.-M. Bony, ?Principle du maximum dans les espaces de Sobolev?, C. R. Acad. Sci. Paris,265 A333-A336 (1967). · Zbl 0164.16803
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.