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

Luigi Ambrosio, Shouhei Honda, Jacobus W. Portegies

研究成果: Article査読

3 被引用数 (Scopus)

抄録

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.

本文言語English
論文番号34
ジャーナルCalculus of Variations and Partial Differential Equations
57
2
DOI
出版ステータスPublished - 2018 4 1

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

フィンガープリント 「Continuity of nonlinear eigenvalues in CD (K, ∞) spaces with respect to measured Gromov–Hausdorff convergence」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル