Fractional Sobolev Spaces and Inequalities

ISBN-13: 9781009254632 / Angielski / Twarda / 2022 / 175 str.

W. D. (Cardiff University) Evans

Opis

Provides an account of fractional Sobolev spaces emphasising applications to famous inequalities. Ideal for graduates and researchers.

Recenzje

'A comprehensive treatise of the theory of fractional Sobolev spaces, defined either on the ambient Euclidean space, or on its generic open subset, and the related inequalities. Striking dissimilarities are discovered in comparison to the classical theory. Contemporary challenging problems are tackled, such as the questions concerning the geometry of underlying domains, the effect of symmetrization techniques, the impact of interpolation, relations to Besov spaces, questions of compactness of embeddings, and more. The book will be of great use to graduate students and researchers of a wide array of scientific interests ranging from partial differential equations and calculus of variations, to approximation and interpolation theory, to the theory of function spaces and related areas. All of the material is accessible through real-variable methods. The only prerequisites, namely basic knowledge of measure theory and Lebesgue integration, will therefore be met by any standard graduate course in real analysis.' Luboš Pick, Charles University, Prague

Spis treści

1. Preliminaries; 2. Classical Sobolev spaces; 3. Fractional Sobolev spaces; 4. Eigenvalues of the fractional p-Laplacian; 5. Classical (local) Hardy inequalities; 6. Fractional analogues; 7. Classical and fractional inequalities of Rellich type; References; Symbol index; Author index; Index of terms.