AI 中文总结
该研究针对带界可测系数的非局部非线性椭圆方程弱解，建立了容量密度条件与一致边界赫尔德估计的等价性，并推导了刻画正则性传递的精细容量估计。
AI 中文摘要
我们研究具有有界可测系数的非局部非线性椭圆方程弱解的边界正则性。主要结果表明，容量密度条件等价于外数据为赫尔德连续时解的一致边界赫尔德估计成立。更一般地，我们推导了关于连续性模的精细容量估计，该估计刻画了正则性如何从外数据传递到解。
英文摘要
We study the boundary regularity of weak solutions to nonlocal nonlinear elliptic equations with bounded measurable coefficients. Our main result establishes that a capacity density condition is equivalent to the validity of a uniform boundary Hölder estimate for solutions with Hölder continuous exterior data. More generally, we derive a fine capacitary estimate on the modulus of continuity that captures how regularity is inherited from the exterior datum to the solution.
Comments26 pages
