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

Luigi Ambrosio, Shouhei Honda, Jacobus W. Portegies

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Samenvatting

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.

Originele taal-2Engels
Artikelnummer34
TijdschriftCalculus of Variations and Partial Differential Equations
Volume57
Nummer van het tijdschrift2
DOI's
StatusGepubliceerd - 1 apr 2018

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