The Boyarsky–Meyers Inequality for the Zaremba Problem for p(∙)-Laplacian

We study the higher integrability of solutions to the Zaremba problem for the p(∙)-Laplacian in a plane domain with Lipschitz boundary. We prove that the Boyarsky–Meyers estimates for solutions are valid under a special ratio between the parts of the Dirichlet and Neumann conditions on the boundary....

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Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2023-08, Vol.274 (4), p.423-440
Main Authors: Alkhutov, Yu. A., Chechkin, G. A.
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Language:English
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Dirichlet problem
Mathematics
Mathematics and Statistics
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description We study the higher integrability of solutions to the Zaremba problem for the p(∙)-Laplacian in a plane domain with Lipschitz boundary. We prove that the Boyarsky–Meyers estimates for solutions are valid under a special ratio between the parts of the Dirichlet and Neumann conditions on the boundary.
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Mathematics and Statistics
title The Boyarsky–Meyers Inequality for the Zaremba Problem for p(∙)-Laplacian
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