On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications

被引：24

作者：

Chems Eddine, Nabil ^{[1
]}

Ragusa, Maria Alessandra ^{[2
,3
]}

Repovs, Dusan D. ^{[4
,5
,6
]}

机构：

[1] Mohammed V Univ, Fac Sci, Dept Math, Lab Math Anal & Applicat, Rabat, Morocco

[2] Univ Catania, Res Ctr Nanomed & Pharmaceut Nanotechnol, Dipartimento Matemat & Informat, NANOMED, Catania, Italy

[3] Ind Univ Ho Chi Minh City, Fac Fundamental Sci, Ho Chi Minh City, Vietnam

[4] Univ Ljubljana, Fac Educ, Ljubljana, Slovenia

[5] Univ Ljubljana, Fac Math & Phys, Ljubljana, Slovenia

[6] Inst Math Phys & Mech, Ljubljana, Slovenia

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2024年 / 27卷 / 02期

关键词：

Sobolev embeddings; Concentration-compactness principle; Anisotropic variable exponent Sobolev spaces; (sic)(x)-Laplacian; Fractional Brezis-Nirenberg problem; LINEAR ELLIPTIC-EQUATIONS; BREZIS-NIRENBERG RESULT; CRITICAL GROWTH; P(X)-LAPLACIAN EQUATIONS; R-N; EXISTENCE; MULTIPLICITY; FUNCTIONALS; EIGENVALUE;

D O I：

10.1007/s13540-024-00246-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We obtain critical embeddings and the concentration-compactness principle for the anisotropic variable exponent Sobolev spaces. As an application of these results,we confirm the existence of and find infinitely many nontrivial solutions for a class of nonlinear critical anisotropic elliptic equations involving variable exponents and two real parameters. With the groundwork laid in this work, there is potential for future extensions, particularly in extending the concentration-compactness principle to anisotropic fractional order Sobolev spaces with variable exponents in bounded domains. This extension could find applications in solving the generalized fractional Brezis-Nirenberg problem.

引用

页码：725 / 756

页数：32

共 49 条

[1] EXISTENCE OF SOLUTIONS FOR A CLASS OF p(x)-LAPLACIAN EQUATIONS INVOLVING A CONCAVE-CONVEX NONLINEARITY WITH CRITICAL GROWTH IN RN [J].