A Brezis-Oswald approach for mixed local and nonlocal operators

Stefano Biagi; Dimitri Mugnai; Eugenio Vecchi

A Brezis-Oswald approach for mixed local and nonlocal operators

Analysis of PDEs 2022-07-27 v3

Authors: Stefano Biagi , Dimitri Mugnai , Eugenio Vecchi

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.

Keywords

mixed local and nonlocal operators sublinear dirichlet problem positive weak solution brezis-oswald approach regularity

Cite

@article{arxiv.2103.11382,
  title  = {A Brezis-Oswald approach for mixed local and nonlocal operators},
  author = {Stefano Biagi and Dimitri Mugnai and Eugenio Vecchi},
  journal= {arXiv preprint arXiv:2103.11382},
  year   = {2022}
}

Comments

The title of the manuscript has been changed after the revision

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