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Mixed Local-nonlocal Operators: Maximum Principles, Eigenvalue Problems and Their Applications by Biswas, Anup; Modasiya, Mitesh is a scholarly article available to read on EtoBox.

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In this article we consider a class of non-degenerate elliptic operators obtained by superpositioning the Laplacian and a general nonlocal operator. We study the existence-uniqueness results for Dirichlet boundary value problems, maximum principles and generalized eigenvalue problems. As applications to these results, we obtain Faber-Krahn inequality and a one-dimensional symmetry result related to the Gibbons' conjecture. The latter results substantially extend the recent results of Biagi et.\ al. [7,9] who consider the operators of the form $-\Delta + (-\Delta)^s$ with $s\in (0, 1)$.

Author

Biswas, Anup; Modasiya, Mitesh

Published

2021

Language

EN