Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

1 results

  • 2 - Elements of Sobolev Space Theory

  • from Part One - Background Material
  • Rupert L. Frank, Ludwig-Maximilians-Universität München, Ari Laptev, Imperial College of Science, Technology and Medicine, London, Timo Weidl, Universität Stuttgart
  • Book:
    Schrödinger Operators: Eigenvalues and Lieb–Thirring Inequalities
    Published online:
    03 November 2022
    Print publication:
    17 November 2022, pp 66-164

  • Summary

    We provide a brief, but self-contained, introduction to the theory of Sobolev spaces. We prove some facts from the calculus with weak derivatives, including product and chain rules. We discuss various kinds of Sobolev inequalities, including those by Gagliardo–Nirenberg, Poincaré, Friedrichs, and Hardy, both on the whole space and on domains, and include some information on their sharp constants. Furthermore, we discuss Rellich’s compactness theorem, the Sobolev extension property of a domain, as well as homogeneous Sobolev spaces.