Stability Estimates for the Lowest Eigenvalue of a Schrödinger Operator

Eric A. Carlen, Rupert L. Frank, Elliott H. Lieb

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


There is a family of potentials that minimize the lowest eigenvalue of a Schrödinger operator 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.

Original languageEnglish (US)
Pages (from-to)63-84
Number of pages22
JournalGeometric and Functional Analysis
Issue number1
StatePublished - Feb 2014

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology


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