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

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

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.

• Jezik: Angleški jezik
• Ključne besede: Sobolev embeddings, concentration-compactness principle, anisotropic variable exponent Sobolev spaces, p(x)-Laplacian, fractional Brezis-Nirenberg problem
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko ; PEF - Pedagoška fakulteta
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Datum objave: 01.04.2024
• Leto izida: 2024
• Št. strani: Str. 725-756
• Številčenje: Vol. 27, iss. 2
• PID: 20.500.12556/RUL-155105
• UDK: 517.9
• ISSN pri članku: 1311-0454
• DOI: 10.1007/s13540-024-00246-8
• COBISS.SI-ID: 186600963
• Datum objave v RUL: 20.03.2024

Gradivo je del revije

• Naslov: Fractional Calculus & Applied Analysis
• Skrajšan naslov: Fract. Calc. Appl. Anal.
• Založnik: De Gruyter, Bulgarian Academy of Sciences. Institute of Mathematics and Informatics
• ISSN: 1311-0454
• COBISS.SI-ID: 18093913

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.