Email this article Regularity of a Boundary Point for the p(x)-Laplacian
- Authors: Alkhutov Y.A.1, Surnachev M.D.2
-
Affiliations:
- A. G. and N. G. Stoletov Vladimir State University
- Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences
- Issue: Vol 232, No 3 (2018)
- Pages: 206-231
- Section: Article
- URL: https://ogarev-online.ru/1072-3374/article/view/241292
- DOI: https://doi.org/10.1007/s10958-018-3870-5
- ID: 241292
Cite item
Open Access
Access granted
Subscription Access
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.
About the authors
Yu. A. Alkhutov
A. G. and N. G. Stoletov Vladimir State University
Author for correspondence.
Email: yurij-alkhutov@yandex.ru
Russian Federation, 87, Gor’kogo St., Vladimir, 600000
M. D. Surnachev
Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences
Email: yurij-alkhutov@yandex.ru
Russian Federation, 4, Miusskaya sq., Moscow, 125047
Supplementary files
