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On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications
ID Chems Eddine, Nabil (Author), ID Ragusa, Maria Alessandra (Author), ID Repovš, Dušan (Author)

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Abstract
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:PEF - Faculty of Education
FMF - Faculty of Mathematics and Physics
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 This link opens in a new window
UDC:517.9
ISSN on article:1311-0454
DOI:10.1007/s13540-024-00246-8 This link opens in a new window
COBISS.SI-ID:186600963 This link opens in a new window
Publication date in RUL:20.03.2024
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Downloads:663
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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 This link opens in a new window

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.

Projects

Funder:ARIS - Slovenian Research and Innovation Agency
Project number:P1-0292
Name:Topologija in njena uporaba

Funder:ARIS - Slovenian Research and Innovation Agency
Project number:J1-4031
Name:Računalniška knjižnica za zavozlane strukture in aplikacije

Funder:ARIS - Slovenian Research and Innovation Agency
Project number:J1-4001
Name:Izbrani problemi iz uporabne in računske topologije

Funder:ARIS - Slovenian Research and Innovation Agency
Project number:N1-0278
Name:Biološka koda vozlov - identifikacija vzorcev vozlanja v biomolekulah z uporabo umetne inteligence

Funder:ARIS - Slovenian Research and Innovation Agency
Project number:N1-0114
Name:Algebrajski odtisi geometrijskih značilnosti v homologiji

Funder:ARIS - Slovenian Research and Innovation Agency
Project number:N1-0083
Name:Forsing, fuzija in kombinatorika odprtih pokritij

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