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Cambridge Tracts in Mathematics Ser.: Fractional Sobolev Spaces and Inequalities by D. E. Edmunds (2022, Hardcover)

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Fractional Sobolev Spaces and Inequalities, Hardcover by Edmunds, D. E.; Evans, W. D., ISBN 1009254634, ISBN-13 9781009254632, Brand New, Free shipping in the US

About this product

Product Identifiers

PublisherCambridge University Press

ISBN-101009254634

ISBN-139781009254632

eBay Product ID (ePID)14057248164

Product Key Features

Number of PagesIX, 157 Pages

Publication NameFractional Sobolev Spaces and Inequalities

LanguageEnglish

SubjectGeneral, Mathematical Analysis

Publication Year2022

TypeTextbook

Subject AreaMathematics

AuthorD. E. Edmunds

SeriesCambridge Tracts in Mathematics Ser.

FormatHardcover

Dimensions

Item Height0.6 in

Item Length9.3 in

Item Width6.2 in

Additional Product Features

LCCN2022-026805

Reviews'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.' Lubos Pick, Charles University, PragueLubos Pick, Charles University, PragueLubos Pick, Charles University, PragueLubos Pick, Charles University, Prague, 'Although introduced in the mid-1950s, the fractional spaces Ws p () have attracted much recent interest because of their many applications, in probability, continuum mechanics, mathematical biology and elsewhere. This monograph is a concise account of the fractional Banach spaces Ws p () and their embedding theorems, and of inequalities such as the fractional analogues of those attributed to Hardy and Rellich in the case of Sobolev spaces. While classical and fractional Sobolev spaces have much in common, it is noted that they differ in important respects, and results are derived from the basic definitions, rather than being inferred from the theory of other function spaces with which Ws p () can be identified, but only when the boundary of is sufficiently regular. The text is a useful guide to the classical and emerging literature.' John Toland, University of Bath

Dewey Edition23

Series Volume NumberSeries Number 230

IllustratedYes

Dewey Decimal515.782

Table Of Content1. 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.

SynopsisA self-contained text providing all the basics of fractional Sobolev spaces. The book provides the background and relevant theory with explanations, alternatives and comparisons, and includes discussion of the Hardy and Rellich inequalities, first in classical format and then in fractional versions. Ideal for researchers and graduate students., 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.

LC Classification NumberQA323.E257 2023