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Second derivatives of solutions of some variational inequalities connected with elliptic nondiagonal systems

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Abstract

Variational inequalities connected with linear elliptic systems of general form are considered. The vector-valued functions, satisfying the variational inequalities in the domain of definition, take values in an arbitrary fixed convex set of the space R N,N>1. It is shown that the second derivatives of the solutions belong to the space L 2,α .An analogous result for a problem with a constraint of special form on the boundary of the domain (the classical Signorini problem) was obtained earlier by Kinderlehrer.

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Authors
  1. A. A. Arkhipova
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Translated from Problemy Matematicheskogo Analiza, No. 11, pp. 6–18, 1990.

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Arkhipova, A.A. Second derivatives of solutions of some variational inequalities connected with elliptic nondiagonal systems. J Math Sci 64, 1225–1233 (1993). https://doi.org/10.1007/BF01098014

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