On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications
Copyright policy )On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications
AbstractWe 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.
- University of Ljubljana Slovenia
- University of Catania Italy
- University of Ljubljana, Faculty of Mathematics and Physics Slovenia
- Mohamed I University Morocco
- Mohammed V University Morocco
Variational methods for second-order elliptic equations, fractional Brezis-Nirenberg problem, Nonlinear elliptic equations, Critical exponents in context of PDEs, Functional Analysis (math.FA), info:eu-repo/classification/udc/517.9, Mathematics - Functional Analysis, Sobolev embeddings, Mathematics - Analysis of PDEs, Variable exponents, Compactness., anisotropic variable exponent Sobolev spaces, FOS: Mathematics, p(x)-Laplacian, 35B33, 35D30, 35J20, 35J60, 46E35, concentration-compactness principle, Weak solutions to PDEs, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, \(\overrightarrow{p}(x)\)-Laplacian, Analysis of PDEs (math.AP)
Variational methods for second-order elliptic equations, fractional Brezis-Nirenberg problem, Nonlinear elliptic equations, Critical exponents in context of PDEs, Functional Analysis (math.FA), info:eu-repo/classification/udc/517.9, Mathematics - Functional Analysis, Sobolev embeddings, Mathematics - Analysis of PDEs, Variable exponents, Compactness., anisotropic variable exponent Sobolev spaces, FOS: Mathematics, p(x)-Laplacian, 35B33, 35D30, 35J20, 35J60, 46E35, concentration-compactness principle, Weak solutions to PDEs, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, \(\overrightarrow{p}(x)\)-Laplacian, Analysis of PDEs (math.AP)
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