We develop 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.
Biagi, S., Dipierro, S., Valdinoci, E., Vecchi, E. (2022). Mixed local and nonlocal elliptic operators: regularity and maximum principles. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 47(3), 585-629 [10.1080/03605302.2021.1998908].
Mixed local and nonlocal elliptic operators: regularity and maximum principles
Vecchi E.
2022
Abstract
We develop 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.| File | Dimensione | Formato | |
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