论文标题
$ p（x）$ - 拉普拉斯方程解决方案的harnack不平等
Harnack inequality for solutions of the $p(x)$-Laplace equation under the precise non-logarithmic Zhikov's conditions
论文作者
论文摘要
我们证明了连续性和Harnack对方程$$ {\ rm div} \ big（| \ nabla u |^{p（x）-2} \，\ nabla u \ big）= 0，\ quad p（x）= p + p + p + p + p + p + p + l \ frac {\ log \ log \ frac {1} {| x-x_ {0} |}}} {\ log \ frac {1} {| x-x_ {0} |}}}}，\ quad l> 0，$ $在确切的非logarith条件下，$ p（x）。
We prove continuity and Harnack's inequality for bounded solutions to the equation $$ {\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 $p(x)$.
