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2008 On the Wiener test for degenerate parabolic equations with non-standard growth condition
Igor I. Skrypnik
Adv. Differential Equations 13(3-4): 229-272 (2008).

Abstract

We investigate the continuity of solutions for general nonlinear parabolic equations of the form \begin{equation*} u_t-\sum_{i=1}^n\frac{\partial}{\partial x_i}\Bigl(\Bigl|\frac{\partial u}{\partial x_i}\Bigr|^{p(x)-2}\frac{\partial u}{\partial x_i}\Bigr)=0,\qquad 2 < p_1\leq p(x)\leq p_2 \end{equation*} near a nonsmooth boundary of a cylindrical domain. We prove the sufficient and necessary condition for regularity of a boundary point in terms of the $p(x)$-capacity.

Citation

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Igor I. Skrypnik. "On the Wiener test for degenerate parabolic equations with non-standard growth condition." Adv. Differential Equations 13 (3-4) 229 - 272, 2008.

Information

Published: 2008
First available in Project Euclid: 18 December 2012

zbMATH: 1170.35055
MathSciNet: MR2482418

Subjects:
Primary: 35K65
Secondary: 35K20, 35K55

Rights: Copyright © 2008 Khayyam Publishing, Inc.

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Vol.13 • No. 3-4 • 2008
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