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Title:On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications
Authors:ID Chems Eddine, Nabil (Author)
ID Ragusa, Maria Alessandra (Author)
ID Repovš, Dušan (Author)
Files:.pdf PDF - Presentation file, download (550,73 KB)
MD5: 1C7FEC19D9755EE00733A54E58C5A3A6
 
URL URL - Source URL, visit https://link.springer.com/article/10.1007/s13540-024-00246-8
 
Language:English
Typology:1.01 - Original Scientific Article
Organization:Logo IMFM - Institute of Mathematics, Physics, and Mechanics
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.
Keywords:Sobolev embeddings, concentration-compactness principle, anisotropic variable exponent Sobolev spaces, p(x)-Laplacian, fractional Brezis-Nirenberg problem
Publication status:Published
Publication version:Version of Record
Publication date:01.04.2024
Year of publishing:2024
Number of pages:str. 725-756
Numbering:Vol. 27, iss. 2
PID:20.500.12556/DiRROS-18484 New window
UDC:517.9
ISSN on article:1311-0454
DOI:10.1007/s13540-024-00246-8 New window
COBISS.SI-ID:186600963 New window
Note:
Publication date in DiRROS:20.03.2024
Views:832
Downloads:662
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CHEMS EDDINE, Nabil, RAGUSA, Maria Alessandra and REPOVŠ, Dušan, 2024, On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications. Fractional Calculus & Applied Analysis [online]. 2024. Vol. 27, no. 2, p. 725–756. [Accessed 7 April 2025]. DOI 10.1007/s13540-024-00246-8. Retrieved from: https://dirros.openscience.si/IzpisGradiva.php?lang=eng&id=18484
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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 New window

Document is financed by a project

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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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.

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