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arXiv · 2208.01970

Harnack inequality for solutions of the $p(x)$-Laplace equation under the precise non-logarithmic Zhikov's conditions

Igor Skrypnik·Yevgeniia Yevgenieva
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Abstract

We prove continuity and Harnack's inequality for bounded solutions to the equation $$ {\rm div}\big(|\nabla u|^{p(x)-2}\,\nabla u \big)=0, \quad p(x)= p + L\frac{\log\log\frac{1}{|x-x_{0}|}}{\log\frac{1}{|x-x_{0}|}},\quad L > 0, $$ under the precise non-logarithmic condition on the function $p(x)$.

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Igor Skrypnik, Yevgeniia Yevgenieva. 2022-08-03. Harnack inequality for solutions of the $p(x)$-Laplace equation under the precise non-logarithmic Zhikov's conditions. https://arxiv.org/abs/2208.01970

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