ENGLISH

Fractional Sobolev Spaces and Inequalities

By D. E. Edmunds , W. D. Evans

Book information

Publisher
Cambridge University Press
Year
2022
ISBN
1009254634, 9781009254632
Language
english
Format
PDF
Filesize
2 MB (1958052 bytes)
Series
Cambridge Tracts in Mathematics, 230
Pages
168\169
Time added
2022-10-21 10:05:07

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.

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