Table of contents : Cover Title page Copyright Dedication Contents Preface Part1: 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 Part2: Fractional Sobolev spaces Fractional Sobolev spaces Embeddings and interpolation Further properties Trace theory Symmetrization Higher order fractional Sobolev spaces Some equivalent seminorms Part3: Applications Interior regularity for the Poisson problem The fractional Laplacian Bibliography Index Back Cover