AN ELLIPTIC BOUNDARY VALUE PROBLEM WITH FRACTIONAL NONLINEARITY

被引：33

作者：

Abatangelo, Nicola ^{[1
]}

Cozzi, Matteo ^{[2
]}

机构：

[1] Goethe Univ Frankfurt Main, Inst Math, Robert Mayer Str 10, D-60325 Frankfurt, Germany

[2] Univ Milan, Dipartimento Matemat Federigo Enriques, Via Saldini 50, I-20133 Milan, Italy

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2021年 / 53卷 / 03期

关键词：

Dirichlet problem; operators of mixed order; comparison principles; fixed-point arguments; large solutions; BLOW-UP SOLUTIONS; DIRICHLET; EQUATIONS;

D O I：

10.1137/20M1342641

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the existence and uniqueness of solutions to second-order elliptic boundary value problems containing a power nonlinearity applied to a fractional Laplacian. We detect the critical power separating the existence from the nonexistence regimes. For the existence results, we make use of a particular class of weighted Sobolev spaces to compensate for boundary singularities which are naturally built in the problem.

引用

页码：3577 / 3601

页数：25

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