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arXiv · 1801.01770

Regularity Results of the Thin Obstacle Problem for the $p(x)$-Laplacian

Sun-sig Byun·Ki-ahm Lee·Jehan Oh·Jinwan Park
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Abstract

We study thin obstacle problems involving the energy functional with $p(x)$-growth. We prove higher integrability and H\"{o}lder regularity for the gradient of minimizers of the thin obstacle problems under the assumption that the variable exponent $p(x)$ is H\"{o}lder continuous.

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Sun-sig Byun, Ki-ahm Lee, Jehan Oh, Jinwan Park. 2018-01-05. Regularity Results of the Thin Obstacle Problem for the $p(x)$-Laplacian. https://arxiv.org/abs/1801.01770

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