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

  • 7 - More on Sharp Lieb–Thirring Inequalities

  • from Part Three - Sharp Constants in Lieb–Thirring Inequalities
  • 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 417-450

  • Summary

    We discuss various independent aspects of sharp Lieb–Thirring inequalities. First, we present an argument of Stubbe which shows that Riesz means of order two and higher approach their semiclassical limit monotonically, thus leading to an alternative proof of sharp Lieb–Thirring inequalities. Next, we discuss the number of negative eigenvalues of Schrödinger operators with radial potentials, following Glaser, Grosse, and Martin. This leads, on the one hand, to a sharp CLR inequality for radial potentials in dimension 4 and, on the other hand, to a counterexample to the Lieb–Thirring conjecture with exponent zero in sufficiently high dimensions. Next, we discuss briefly an approach that disproves the Lieb–Thirring conjecture in a certain range of positive exponents. Finally, we discuss the Lieb–Thirring inequality with exponent one in its dual formulation, also known as kinetic energy inequality, in which it enters in many applications.