Abstract
Variational inequalities, connected with quasilinear elliptic systems with a diagonal principal part and a quadratic growth along the gradient, are considered. On the boundary of the domain convex constraints are imposed on the solution. The Hölder continuity of the solution up to the boundary of the domain is proved.
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Literature cited
A. A. Arkhipova and N. N. Ural'tseva, “The regularity of the solutions of diagonal elliptic systems under convex constraints on the boundary of the domain,” J. Sov. Math.,40, No. 5 (1980).
A. A. Arkhipova and N. N. Ural'tseva, “The regularity of the solutions of variational inequalities with convex constraints on the boundary of the domain for nonlinear operators with a diagonal principal part,” Vestn. Leningr. Univ., Ser. Mat., No. 3, 13–19 (1987).
O. A. Ladyzhenskaya and N. N. Ural'tseva, “A survey of results on the solvability of boundary-value problems for uniformly elliptic and parabolic second-order equations having unbounded singularities,” Usp. Mat. Nauk,41, No. 5, 59–83 (1986).
O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations [in Russian], Nauka, Moscow (1973).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 163, pp. 5–16, 1987.
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Arkhipova, A.A., Ural'tseva, N.N. Limit smoothness of the solutions of variational inequalities under convex constraints on the boundary of the domain. J Math Sci 49, 1121–1128 (1990). https://doi.org/10.1007/BF02208707
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DOI: https://doi.org/10.1007/BF02208707