Abstract
We prove sufficient conditions for the existence of a solution of a “strong” nonlinear variational inequality of parabolic type. The theory can be used for solving parabolic equations with one-sided boundary conditions. As an example, we prove the existence of a solution of a “strong” parabolic variational inequality with p-Laplacian in the Sobolev space L p (0, T, W p 1 (Ω)), p ∈ [2, ∞).
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