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arXiv · 2308.05559

On higher integrability for $p(x)$-Laplacian equations with drift

Jingya Chen·Bin Guo·Baisheng Yan
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Abstract

In this paper, we study the higher integrability for the gradient of weak solutions of $p(x)$-Laplacians equation with drift terms. We prove a version of generalized Gehring's lemma under some weaker condition on the modulus of continuity of variable exponent $p(x)$ and present a modified version of Sobolev-Poincaré inequality with such an exponent. When $p(x)>2$ we derive the reverse Hölder inequality with a proper dependence on the drift and force terms and establish a specific high integrability result. Our condition on the exponent $p(x)$ is more specific and weaker than the known conditions and our results extend some results on the $p(x)$-Laplacian equations without drift terms.

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Jingya Chen, Bin Guo, Baisheng Yan. 2023-08-10. On higher integrability for $p(x)$-Laplacian equations with drift. https://arxiv.org/abs/2308.05559

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