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

Chems Eddine, Nabil (author), Ragusa, Maria Alessandra (author), Repovš, Dušan (author)

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.

• Language: English
• Keywords: Sobolev embeddings, concentration-compactness principle, anisotropic variable exponent Sobolev spaces, p(x)-Laplacian, fractional Brezis-Nirenberg problem
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics; PEF - Faculty of Education
• Publication status: Published
• Publication version: Version of Record
• Publication date: 01.04.2024
• Year: 2024
• Number of pages: Str. 725-756
• Numbering: Vol. 27, iss. 2
• PID: 20.500.12556/RUL-155105
• UDC: 517.9
• ISSN on article: 1311-0454
• DOI: 10.1007/s13540-024-00246-8
• COBISS.SI-ID: 186600963
• Publication date in RUL: 20.03.2024

Record is a part of a journal

• Title: Fractional Calculus & Applied Analysis
• Shortened title: Fract. Calc. Appl. Anal.
• Publisher: De Gruyter, Bulgarian Academy of Sciences. Institute of Mathematics and Informatics
• ISSN: 1311-0454
• COBISS.SI-ID: 18093913

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.