, Volume 40, Issue 5, pp 591-598

Regularity of the solutions of diagonal elliptic systems under convex constraints on the boundary of the domain

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Abstract

One investigates the smoothness of the solutions of variational inequalities, connected with second-order linear diagonal elliptic systems under convex constraints on the solution at the boundary of the domain. One establishes the Holder continuity of the first derivatives of the solutions up to the boundary of the domain.

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta m. V. A. Steklova AN SSSR, Vol. 152, pp. 5–17, 1986.