论文标题
全球分数caccioppoli型估计用于针对非线性椭圆问题的解决方案的估计值
A global fractional Caccioppoli-type estimate for solutions to nonlinear elliptic problems with measure data
论文作者
论文摘要
我们通过分数Caccioppoli型估计值证明了全球分数可不同性结果，用于用于测量数据的非线性椭圆问题解决方案。实际上，这项工作的灵感来自最近的论文[B. Avelin，T。Kuusi，G。Mingione，{\ em nonearcalderón-Zygmund理论在限制案例中}，Arch。合理的。机械。肛门。 {\ bf 227}（2018），663--714]，它专门用于局部分数规律性，以提供具有右手量度的非线性椭圆方程的解决方案，类型为$ - \ mathrm {div} \，\ Mathcal，\ mathcal {a}（a a}（a abla u）（\ nabla u）=μ=μ$ in nimise n limitie n in the the the the liming case in n limitie n in the limitie n in the limitie n in the n liming case in。作为对识别功能类别的最新结果的贡献，可以定义解决此类问题的解决方案，我们在这项工作中的目的是在加权分数Sobolev空间的设置中建立全球规则性结果，其中权重是距离光滑域边界的距离函数的力量。
We prove a global fractional differentiability result via the fractional Caccioppoli-type estimate for solutions to nonlinear elliptic problems with measure data. This work is in fact inspired by the recent paper [B. Avelin, T. Kuusi, G. Mingione, {\em Nonlinear Calderón-Zygmund theory in the limiting case}, Arch. Rational. Mech. Anal. {\bf 227}(2018), 663--714], that was devoted to the local fractional regularity for the solutions to nonlinear elliptic equations with right-hand side measure, of type $-\mathrm{div}\, \mathcal{A}(\nabla u) = μ$ in the limiting case. Being a contribution to recent results of identifying function classes that solutions to such problems could be defined, our aim in this work is to establish a global regularity result in a setting of weighted fractional Sobolev spaces, where the weights are powers of the distance function to the boundary of the smooth domains.
