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Mathematics > Analysis of PDEs

arXiv:1301.5032 (math)
[Submitted on 21 Jan 2013 (v1), last revised 14 May 2013 (this version, v2)]

Title:Stability estimates for the lowest eigenvalue of a Schrödinger operator

Authors:Eric A. Carlen, Rupert L. Frank, Elliott H. Lieb
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Abstract:There is a family of potentials that minimize the lowest eigenvalue of a Schrödinger eigenvalue under the constraint of a given L^p norm of the potential. We give effective estimates for the amount by which the eigenvalue increases when the potential is not one of these optimal potentials. Our results are analogous to those for the isoperimetric problem and the Sobolev inequality. We also prove a stability estimate for Hölder's inequality, which we believe to be new.
Comments: 20 pages; reference added; minor change in the statement and proof of Theorem 3.1
Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph); Spectral Theory (math.SP)
Cite as: arXiv:1301.5032 [math.AP]
  (or arXiv:1301.5032v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1301.5032

Submission history

From: Rupert Frank [view email]
[v1] Mon, 21 Jan 2013 22:49:23 UTC (18 KB)
[v2] Tue, 14 May 2013 19:32:25 UTC (18 KB)
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