Abstract

We prove the higher integrability of the gradient of solutions of the Zaremba problem in a bounded strongly Lipschitz domain for an inhomogeneous \(p(\,\cdot\,)\)-Laplace equation with a variable exponent \(p\) having a logarithmic continuity modulus.

中文翻译：

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$$p(\,\cdot\,)$$ -拉普拉斯方程的多维 Zaremba 问题。 Boyarsky-Meyers 估计

摘要

我们证明了 Zaremba 问题的梯度解的梯度在有界强 Lipschitz 域中对于非齐次\(p(\,\cdot\,)\) -拉普拉斯方程（其变量指数\(p\)具有更高的可积性）对数连续性模量。