A family of nonlocal degenerate operators: maximum principles and related properties

被引：0
|
作者：
Schiera, Delia [1 ]
机构：
[1] Univ Lisbon, Inst Super Tecn, Dept Matemat, Av Rovisco Pais, P-1049001 Lisbon, Portugal
来源：
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2024年 / 31卷 / 01期
关键词：
Maximum and comparison principles; Fully nonlinear degenerate elliptic PDE; Nonlocal operators; Eigenvalue problem; VISCOSITY SOLUTIONS;
D O I：
10.1007/s00030-023-00892-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider a class of fully nonlinear nonlocal degenerate elliptic operators which are modeled on the fractional Laplacian and converge to the truncated Laplacians. We investigate the validity of (strong) maximum and minimum principles, and their relation with suitably defined principal eigenvalues. We also show a Hopf type Lemma, the existence of solutions for the corresponding Dirichlet problem, and representation formulas in some particular cases.
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页数：31
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