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- Title
On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications.
- Authors
Chems Eddine, Nabil; Ragusa, Maria Alessandra; Repovš, Dušan D.
- 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.
- Subjects
SOBOLEV spaces; EXPONENTS
- Publication
Fractional Calculus & Applied Analysis, 2024, Vol 27, Issue 2, p725
- ISSN
1311-0454
- Publication type
Article
- DOI
10.1007/s13540-024-00246-8