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Regularity of a Boundary Point for the p(x)-Laplacian

Regularity of a Boundary Point for the p(x)-Laplacian We study the behavior of solutions to the Dirichlet problem for the p(x)-Laplacian with a continuous boundary function. We prove the existence of a weak solution under the assumption that p is separated from 1 and ∞. We present a necessary and sufficient Wiener type condition for regularity of a boundary point provided that the exponent p has the logarithmic modulus of continuity at this point. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Mathematical Sciences Springer Journals

Regularity of a Boundary Point for the p(x)-Laplacian

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References (26)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
1072-3374
eISSN
1573-8795
DOI
10.1007/s10958-018-3870-5
Publisher site
See Article on Publisher Site

Abstract

We study the behavior of solutions to the Dirichlet problem for the p(x)-Laplacian with a continuous boundary function. We prove the existence of a weak solution under the assumption that p is separated from 1 and ∞. We present a necessary and sufficient Wiener type condition for regularity of a boundary point provided that the exponent p has the logarithmic modulus of continuity at this point.

Journal

Journal of Mathematical SciencesSpringer Journals

Published: Jun 2, 2018

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