Mixed local and nonlocal elliptic operators: regularity and maximum principles

Stefano Biagi, Serena Dipierro, Enrico Valdinoci, Eugenio Vecchi

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

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.

Original languageEnglish
JournalCommunications in Partial Differential Equations
DOIs
Publication statusE-pub ahead of print - 2021

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