Differential Operators on Spaces of Variable Integrability
Edition: First edition
Publisher: World Scientific Publishing Company (WSPC)
Published: June 26, 2014
Place of publication: Singapore, Hong Kong
Language: eng
Format: Paperback
Number of pages: 222
ISBN-13: 9789814596312
Copyright date: ©2014
Notes: 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.