Abstract
In a curvilinear quadrangle one considers an elliptic operator with linear principal terms and discontinuous leading coefficients. One investigates the solution of a variational inequality with a constraint on the derivatives, tangent to the boundary and to the discontinuity lines of the coefficients. On certain parts of the boundary one imposes the first boundary condition and on others a condition on a directional derivative. One proves the existence of a solution with square summable second derivatives at each point of the subdomains where the leading coefficients are smooth.
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Translated from Problemy Matematicheskogo Analiza, No. 10, pp. 83–92, 1986.
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Solomyak, T.E. Properties of the solutions of a certain class of variational inequalities. J Math Sci 45, 1173–1180 (1989). https://doi.org/10.1007/BF01096149
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DOI: https://doi.org/10.1007/BF01096149