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
相关论文
共 54 条
  • [1] AN ELLIPTIC BOUNDARY VALUE PROBLEM WITH FRACTIONAL NONLINEARITY
    Abatangelo, Nicola
    Cozzi, Matteo
    [J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2021, 53 (03) : 3577 - 3601
  • [2] A NOTE ON THE PROBLEM -DELTA-U=+U/U/2-STAR-2
    AMBROSETTI, A
    STRUWE, M
    [J]. MANUSCRIPTA MATHEMATICA, 1986, 54 (04) : 373 - 379
  • [3] [Anonymous], 1997, Adv. Differential Equations
  • [4] [Anonymous], 1998, Differential Integral Equations
  • [5] [Anonymous], 1995, Differ. Integral Equ.
  • [6] The second bifurcation branch for radial solutions of the Brezis-Nirenberg problem in dimension four
    Arioli, Gianni
    Gazzola, Filippo
    Grunau, Hans-Christoph
    Sassone, Edoardo
    [J]. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2008, 15 (1-2): : 69 - 90
  • [7] AZORERO JPG, 1987, COMMUN PART DIFF EQ, V12, P1389
  • [8] A critical fractional equation with concave convex power nonlinearities
    Barrios, B.
    Colorado, E.
    Servadei, R.
    Soria, F.
    [J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2015, 32 (04): : 875 - 900
  • [9] CRITICAL EXPONENTS AND MULTIPLE CRITICAL DIMENSIONS FOR POLYHARMONIC OPERATORS
    BERNIS, F
    GRUNAU, HC
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1995, 117 (02) : 469 - 486
  • [10] A Faber-Krahn inequality for mixed local and nonlocal operators
    Biagi, Stefano
    Dipierro, Serena
    Valdinoci, Enrico
    Vecchi, Eugenio
    [J]. JOURNAL D ANALYSE MATHEMATIQUE, 2023, 150 (02): : 405 - 448
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