Abstract
We consider nonlinear elliptic second-order variational inequalities with degenerate (with respect to the spatial variable) and anisotropic coefficients and L 1-data. We study the cases where the set of constraints belongs to a certain anisotropic weighted Sobolev space and to a larger function class. In the first case, some new properties of T-solutions and shift T-solutions of the investigated variational inequalities are established. Moreover, the notion of W 1,1-regular T-solution is introduced, and a theorem of existence and uniqueness of such a solution is proved. In the second case, we introduce the notion of T-solution of the variational inequalities under consideration and establish conditions of existence and uniqueness of such a solution.
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Original Russian Text © A.A. Kovalevsky, 2015, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2015, Vol. 21, No. 1.
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Kovalevsky, A.A. Toward the L 1-theory of degenerate anisotropic elliptic variational inequalities. Proc. Steklov Inst. Math. 292 (Suppl 1), 156–172 (2016). https://doi.org/10.1134/S0081543816020139
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DOI: https://doi.org/10.1134/S0081543816020139