A Brezis-Oswald approach for mixed local and nonlocal operators

被引：37

作者：

Biagi, Stefano ^{[1
]}

Mugnai, Dimitri ^{[2
]}

Vecchi, Eugenio ^{[3
]}

机构：

[1] Politecn Milan, Dipartimento Matemat, Via Bonardi 9, I-20133 Milan, Italy

[2] Univ Tuscia, Dipartimento Ecol & Biol DEB, Largo dellUniv, I-01100 Viterbo, Italy

[3] Univ Bologna, Dipartimento Matemat, Piazza Porta San Donato 5, Bologna, Italy

来源：

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2024年 / 26卷 / 02期

关键词：

Operators of mixed order; p-sublinear Dirichlet problems; existence and uniqueness of solutions; strong maximum principle; L-infinity-estimate; P-LAPLACIANS; EIGENVALUE; EXISTENCE;

D O I：

10.1142/S0219199722500572

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. L-p,L-s = -Delta(p) + (-Delta)(p)(s). Our main result is resemblant to the celebrated work by Brezis-Oswald [Remarks on sublinear elliptic equations, Nonlinear Anal. 10 (1986) 55-64]. In addition, we prove a regularity result of independent interest.

引用

页数：28

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