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
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页码：15 / 37
页数：23
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