In this paper we establish the local regularity estimates in Besov spaces of weak solutions for the elliptic $p(x)$-Laplacian equation with the logarithmic growth in divergence form$\text{div}({\left|\mathrm{\nabla }u\right|}^{p(x)-2}\ln (e+\left|\mathrm{\nabla }u\right|)\mathrm{\nabla }u)=\text{div}\mathbf{F}$ under some proper assumptions on the functions $p(x)$ and F. Moreover, it is worth noting that our results improve the known results for these types of equations.

中文翻译：

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具有对数增长的椭圆p（x）-Laplacian方程的Besov正则性估计。

在本文中，我们在椭圆的弱解的Besov空间中建立了局部正则估计 $p（X）$-Laplacian方程，对数增长为散度形式$\text{div}（{\left|\mathrm{\nabla }ü\right|}^{p（X）-2}\ln （Ë+\left|\mathrm{\nabla }ü\right|）\mathrm{\nabla }ü）=\text{div}\mathbf{F}$ 在适当的功能假设下 $p（X）$和˚F。此外，值得注意的是，我们的结果改进了这类方程的已知结果。