Description

Book Synopsis
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 book can serve as a reference for mathematicians working in the calculus of variations and partial differential equations as well as for researchers in other disciplines.

Table of Contents
  • 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

A First Course in Fractional Sobolev Spaces

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    A Paperback by Giovanni Leoni

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      Book details

      Publisher American Mathematical Society
      Published 5/30/2023 12:00:00 AM
      ISBN-13 9781470472535
      978-1470472535
      ISBN-10 1470472538

      Description

      Book Synopsis
      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 book can serve as a reference for mathematicians working in the calculus of variations and partial differential equations as well as for researchers in other disciplines.

      Table of Contents
      • 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

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