Continuity of nonlinear eigenvalues in CD (K, ∞) spaces with respect to measured Gromov–Hausdorff convergence

Luigi Ambrosio, Shouhei Honda, Jacobus W. Portegies

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)
3 Downloads (Pure)

Abstract

In this note we prove in the nonlinear setting of CD (K, ∞) spaces the stability of the Krasnoselskii spectrum of the Laplace operator -Δ under measured Gromov–Hausdorff convergence, under an additional compactness assumption satisfied, for instance, by sequences of CD (K, N) metric measure spaces with uniformly bounded diameter. Additionally, we show that every element λ in the Krasnoselskii spectrum is indeed an eigenvalue, namely there exists a nontrivial u satisfying the eigenvalue equation -Δu=λu.

Original languageEnglish
Article number34
JournalCalculus of Variations and Partial Differential Equations
Volume57
Issue number2
DOIs
Publication statusPublished - 1 Apr 2018

Keywords

  • 49J35
  • 49J52
  • 49R05
  • 58J35

Fingerprint

Dive into the research topics of 'Continuity of nonlinear eigenvalues in CD (K, ∞) spaces with respect to measured Gromov–Hausdorff convergence'. Together they form a unique fingerprint.

Cite this