Differential Operators on Spaces of Variable Integrability

1. Preliminaries. 1.1. The geometry of Banach spaces. 1.2. Spaces with variable exponent -- 2. Sobolev spaces with variable exponent. 2.1. Definition and functional-analytic properties. 2.2. Sobolev embeddings. 2.3. Compact embeddings. 2.4. Riesz potentials. 2.5. Poincare-type inequalities. 2.6. Embeddings. 2.7. Holder spaces with variable exponents. 2.8. Compact embeddings revisited -- 3. The p[symbol]-Laplacian. 3.1. Preliminaries. 3.2. The p[symbol]-Laplacian. 3.3. Stability with respect to integrability -- 4. Eigenvalues. 4.1. The derivative of the modular. 4.2. Compactness and Eigenvalues. 4.3. Modular Eigenvalues. 4.4. Stability with respect to the exponent. 4.5. Convergence properties of the Eigenfunctions -- 5. Approximation on Lp spaces. 5.1. s-numbers and n-widths. 5.2. A Sobolev embedding. 5.3. Integral operators

• | Author: David Eric Edmunds, Jan Lang, Osvaldo David Mendez
• | Publisher: World Scientific Publishing Company Incorporated
• | Publication Date: Aug 26, 2014
• | Number of Pages: 208 pages
• | Language: English
• | Binding: Hardcover
• | ISBN-10: 9814596310
• | ISBN-13: 9789814596312