20.500.12556/DiRROS-18484 On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications 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. Sobolev embeddings concentration-compactness principle anisotropic variable exponent Sobolev spaces p(x)-Laplacian fractional Brezis-Nirenberg problem true false true Angleški jezik Ni določen Neznano 2024-03-20 10:09:21 2024-03-20 10:09:21 2024-03-21 03:35:37 0000-00-00 00:00:00 2024 0 0 str. 725-756 iss. 2 Vol. 27 Apr. 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2024-04-01 517.9 1311-0454 10.1007/s13540-024-00246-8 186600963 s13540-024-00246-8-1.pdf s13540-024-00246-8-1.pdf 1 1C7FEC19D9755EE00733A54E58C5A3A6 406690c9af339df1823bfc011d4dbcd5b344452e77e57072624e29621f64d37e bad4b11d-e699-11ee-9dd4-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=25186 https://link.springer.com/article/10.1007/s13540-024-00246-8 1 8b7962d0-e699-11ee-9dd4-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=25185 Inštitut za matematiko, fiziko in mehaniko 0 0 0