THE BREZIS-NIRENBERG PROBLEM FOR MIXED LOCAL AND NONLOCAL OPERATORS

被引：0
|
作者：
Biagi, Stefano [1 ,2 ]
机构：
[1] Univi Bologna, Dipartimento Matemat, Bologna, Italy
[2] Politecn Milan, Via Bonardi 9, I-20133 Milan, Italy
来源：
BRUNO PINI MATHEMATICAL ANALYSIS SEMINAR | 2023年 / 14卷 / 01期
关键词：
Operators of mixed order; Sobolev inequality; critical exponents; existence theory; MULTIPLE CRITICAL DIMENSIONS; CRITICAL SOBOLEV; ELLIPTIC-EQUATIONS; CRITICAL EXPONENTS; POSITIVE SOLUTIONS; LAPLACE EQUATIONS; CRITICAL GROWTH; R-N; EXISTENCE; BIFURCATION;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this note we present some existence results, in the spirit of the celebrated paper by Brezis and Nirenberg (CPAM, 1983), for a perturbed critical problem driven by a mixed local and nonlocal linear operator. We develop an existence theory, both in the case of linear and superlinear perturbations; moreover, in the particular case of linear perturbations we also investigate the mixed Sobolev inequality associated with this problem, detecting the optimal constant, which we show that is never achieved.
引用
收藏
页码：15 / 37
页数：23
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