Ukrainian Mathematical Bulletin

Volume 1, Issue 3, 2004 pp. 377-406.

On the Necessity of the Wiener Condition for Nonlinear Singular Parabolic Equations

Authors: Igor I. Skrypnik
Author institution: Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine, R. Luxembourg Str., 74, Donetsk 83114, Ukraine

Summary: We investigate the continuity of solutions of nonlinear parabolic equations near the nonsmooth boundary of a cylindrical domain. As a particular case, one can consider a parabolic equation with a $p$-Laplace operator in the main part $(p 2)$. We prove a necessary condition for the regularity of a boundary point in terms of $p$-capacity.

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