We consider a pseudo-differential equation driven by the fractional $p$-Laplacian with $p\ge 2$ (degenerate case), with a bounded reaction $f$ and Dirichlet type conditions in a smooth domain $\Omega$. By means of barriers, a nonlocal superposition principle, and the comparison principle, we prove that any weak solution $u$ of such equation exhibits a weighted H\"older regularity up to the boundary, that is, $u/d^s\in C^\alpha(\overline\Omega)$ for some $\alpha\in(0,1)$, $d$ being the distance from the boundary.

中文翻译：

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退化分数 p-Laplacian 的精细边界正则性

我们考虑由分数 $p$-Laplacian 驱动的伪微分方程，具有 $p\ge 2$（退化情况），在光滑域 $\Omega$ 中具有有界反应 $f$ 和 Dirichlet 类型条件。通过障碍、非局部叠加原理和比较原理，我们证明了此类方程的任何弱解 $u$ 都表现出一个加权的 H\" 更旧的正则性直到边界，即 $u/d^s\在 C^\alpha(\overline\Omega)$ 对于某些 $\alpha\in(0,1)$，$d$ 是与边界的距离。