Abstract
We investigate the continuity of solutions of quasilinear parabolic equations in the neighborhood of the nonsmooth boundary of a cylindrical domain. As a special case, one can consider the equation \(\frac{{\partial u}}{{\partial t}} - \Delta _p u = 0\) with the p-Laplace operator Δp. We prove a sufficient condition for the regularity of a boundary point in terms of C p-capacity.
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Skrypnik, I.I. Regularity of a Boundary Point for Degenerate Parabolic Equations with Measurable Coefficients. Ukrainian Mathematical Journal 52, 1768–1786 (2000). https://doi.org/10.1023/A:1010487306017
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DOI: https://doi.org/10.1023/A:1010487306017