We study asymptotically regular elliptic equations with $L^{p\left(x\right)}$-logarithmic growth under the assumptions that the variable exponent satisfies strong log-Hölder continuity and the underlying domain is Reifenberg flat. To ensure a global Calderón–Zygmund estimate for such asymptotically regular problem, we make use of approximating the solutions for asymptotically regular problem by the solutions for regular problem while the gradients of the solutions close to infinity.

中文翻译：

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具有 Lp(x) 对数增长的渐近规则椭圆方程的 Calderón–Zygmund 估计

我们研究渐近规则椭圆方程${\mathrm{大号}}^{p\left(X\right)}$- 假设变量指数满足强 log-Hölder 连续性且基础域为 Reifenberg flat 的假设下的对数增长。为了确保对此类渐近正则问题的全局 Calderón-Zygmund 估计，我们利用正则问题的解来逼近渐近正则问题的解，同时解的梯度接近无穷大。