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arXiv · 2103.11382

A Brezis-Oswald approach for mixed local and nonlocal operators

Stefano Biagi·Dimitri Mugnai·Eugenio Vecchi
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Abstract

In this paper we provide necessary and sufficient conditions for the existence of a unique positive weak solution for some sublinear Dirichlet problems driven by the sum of a quasilinear local and a nonlocal operator, i.e., $$\mathcal{L}_{p,s} = -\Delta_p + (-\Delta)^s_p.$$ Our main result is resemblant to the celebrated work by Brezis-Oswald [10]. In addition, we prove a regularity result of independent interest.

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Stefano Biagi, Dimitri Mugnai, Eugenio Vecchi. 2021-03-21. A Brezis-Oswald approach for mixed local and nonlocal operators. https://arxiv.org/abs/2103.11382

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