Fractional Sobolev Spaces and Inequalities (Cambridge Tracts in Mathematics)

Edmunds, D. E./ Evans, W. D.

Cambridge University Press（2022/10発売）

• 製本 Hardcover:ハードカバー版／ページ数 175 p.
• 言語 ENG
• 商品コード 9781009254632
• DDC分類 515.782

Full Description

The fractional Sobolev spaces studied in the book were introduced in the 1950s by Aronszajn, Gagliardo and Slobodeckij in an attempt to fill the gaps between the classical Sobolev spaces. They provide a natural home for solutions of a vast, and rapidly growing, number of questions involving differential equations and non-local effects, ranging from financial modelling to ultra-relativistic quantum mechanics, emphasising the need to be familiar with their fundamental properties and associated techniques. Following an account of the most basic properties of the fractional spaces, two celebrated inequalities, those of Hardy and Rellich, are discussed, first in classical format (for which a survey of the very extensive known results is given), and then in fractional versions. This book will be an Ideal resource for researchers and graduate students working on differential operators and boundary value problems.

Contents

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.