Mixed local-nonlocal operators: maximum principles, eigenvalue problems and their applications

Anup Biswas; Mitesh Modasiya

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arXiv · 2110.06746

Mixed local-nonlocal operators: maximum principles, eigenvalue problems and their applications

Anup Biswas·Mitesh Modasiya

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Abstract

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 $s\in (0, 1)$.

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Anup Biswas, Mitesh Modasiya. 2021-10-13. Mixed local-nonlocal operators: maximum principles, eigenvalue problems and their applications. https://arxiv.org/abs/2110.06746

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