Woodslane | Book - 9781470468989

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A First Course in Fractional Sobolev Spaces

ISBN-13: 9781470468989
Publisher: AMERICAN MATHEMATICAL SOCIETY
Imprint: AMERICAN MATHEMATICAL SOCIETY
By Giovanni Leoni
Price: AUD $347.00
Stock: 0 in stock
Availability: This book is temporarily out of stock, order will be despatched as soon as fresh stock is received.
Local release date: 29/08/2023
Format: Hardback (254.00mm X 178.00mm) 579 pages Weight: 554g
Categories: Calculus [PBKA]

Description
Author Biography
Table of Contents
Google Preview: This book provides a gentle introduction to fractional Sobolev spaces which play a central role in the calculus of variations, partial differential equations, and harmonic analysis. The first part deals with fractional Sobolev spaces of one variable. It covers the definition, standard properties, extensions, embeddings, Hardy inequalities, and interpolation inequalities. The second part deals with fractional Sobolev spaces of several variables. The author studies completeness, density, homogeneous fractional Sobolev spaces, embeddings, necessary and sufficient conditions for extensions, Gagliardo-Nirenberg type interpolation inequalities, and trace theory. The third part explores some applications: interior regularity for the Poisson problem with the right-hand side in a fractional Sobolev space and some basic properties of the fractional Laplacian. The first part of the book is accessible to advanced undergraduates with a strong background in integration theory; the second part, to graduate students having familiarity with measure and integration and some functional analysis. Basic knowledge of Sobolev spaces would help, but is not necessary. The book can also serve as a reference for mathematicians working in the calculus of variations and partial differential equations as well as for researchers in other disciplines with a solid mathematics background. It contains several exercises and is self-contained.; Giovanni Leoni, Carnegie Mellon University, Pittsburgh, PA.; Fractional Sobolev spaces in one dimension: Fractional Sobolev spaces in one dimension Embeddings and interpolation A bit of wavelets Rearrangements Higher order fractional Sobolev spaces in one dimension Fractional Sobolev spaces: Fractional Sobolev spaces Embeddings and interpolation Further properties Trace theory Symmetrization Higher order fractional Sobolev spaces Some equivalent seminorms Applications: Interior regularity for the Poisson problem The fractional Laplacian Bibliography Index; Google Preview content

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A First Course in Fractional Sobolev Spaces