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

Luigi Ambrosio, Shouhei Honda, Jacobus W. Portegies

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 34 Calculus of Variations and Partial Differential Equations 57 2 https://doi.org/10.1007/s00526-018-1315-0 Published - 2018 4 1

## ASJC Scopus subject areas

• Analysis
• Applied Mathematics