The Compact Embeddings and the Concentration-Compactness Principles for Anisotropic Variable Exponent Sobolev Spaces and Applications
Copyright policy )The Compact Embeddings and the Concentration-Compactness Principles for Anisotropic Variable Exponent Sobolev Spaces and Applications
Abstract In this paper, we present new results about the compact embeddings of anisotropic variable exponent Sobolev spaces into variable Lebesgue spaces. We also refine and extend the concentration–compactness principle to trace embeddings in these spaces. Using these results, we prove the existence of infinitely many nontrivial solutions for a class of nonlinear anisotropic Neumann problems with two critical variable exponents.
\( \overrightarrow{p}(x)\)-Laplacian, Variational methods for second-order elliptic equations, anisotropic variable exponent Sobolev spaces, compact embedding, concentration-compactness principle, Nonlinear elliptic equations, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Weak solutions to PDEs, Critical exponents in context of PDEs
\( \overrightarrow{p}(x)\)-Laplacian, Variational methods for second-order elliptic equations, anisotropic variable exponent Sobolev spaces, compact embedding, concentration-compactness principle, Nonlinear elliptic equations, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Weak solutions to PDEs, Critical exponents in context of PDEs
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