论文标题
混合本地和非局部椭圆操作员：规律性和最大原则
Mixed local and nonlocal elliptic operators: regularity and maximum principles
论文作者
论文摘要
我们从本文开始进行一项系统的研究，对椭圆算子的叠加具有不同的订单，将经典和分数场景混合在一起。出于具体性，我们专注于拉普拉斯主义者和分数laplacian的总和，并提供结构性结果，包括存在，最大原理（用于弱和经典解决方案），内部Sobolev的规律性和Lipschitz类型的边界规律性。
We start in this paper a systematic study of the superpositions of elliptic operators with different orders, mixing classical and fractional scenarios. For concreteness, we focus on the sum of the Laplacian and the fractional Laplacian, and we provide structural results, including existence, maximum principles (both for weak and classical solutions), interior Sobolev regularity and boundary regularity of Lipschitz type.
