混合局部-非局部型拟线性算子的全局梯度正则性与Hopf引理
Global gradient regularity and a Hopf lemma for quasilinear operators of mixed local-nonlocal type
AI总结：
本文针对p-Laplacian与分数阶(s, q)-Laplacian之和构成的混合局部-非局部拟线性算子，在边界仅为C^{1, α}且p > s q的条件下，证明了弱解到边界的C^{1, θ}正则性，并建立了正上解的Hopf型引理。
AI中文摘要：
我们研究以p-Laplacian与分数阶(s, q)-Laplacian之和为模型的混合局部-非局部拟线性算子的一些正则性问题。在右端项和外部数据满足适当假设的条件下，我们证明Dirichlet问题的弱解具有直到边界的C^{1, θ}正则性。此外，我们建立了正上解的Hopf型引理。这两个结果都只要求参考区域的边界属于C^{1, α}类，而对于正则性结果，我们还需要p > s q。
英文摘要：
We address some regularity issues for mixed local-nonlocal quasilinear operators modeled upon the sum of a $p$-Laplacian and of a fractional $(s, q)$-Laplacian. Under suitable assumptions on the right-hand sides and the outer data, we show that weak solutions of the Dirichlet problem are $C^{1, θ}$-regular up to the boundary. In addition, we establish a Hopf type lemma for positive supersolutions. Both results hold assuming the boundary of the reference domain to be merely of class $C^{1, α}$, while for the regularity result we also require that $p > s q$.
