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.
|ジャーナル||Calculus of Variations and Partial Differential Equations|
|出版ステータス||Published - 2018 4 1|
ASJC Scopus subject areas
- Applied Mathematics