Abstract
For the equation Au=f(x) in the domain Ω⊂Rn, where A is a linear second-order elliptic operator, under conditions of Signorini type on the boundary of the domain Ω, one proves the boundedness of the Hölder continuity of the first derivatives of the solution under the assumption that fɛ Lq(Ω), q>n. The results are applied to the investigation of the regularity of the solutions of variational inequalities in the case of quasilinear operators.
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Translated from Problemy Matematicheskogo Analiza, No. 10, pp. 92–105, 1986.
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Ural'tseva, N.N. An estimate of the derivatives of the solutions of variational inequalities on the boundary of the domain. J Math Sci 45, 1181–1191 (1989). https://doi.org/10.1007/BF01096150
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DOI: https://doi.org/10.1007/BF01096150