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Moltiplicatori spettrali per l'operatore di Ornstein-Uhlenbeck

Giancarlo Mauceri (2004)

Bollettino dell'Unione Matematica Italiana

Questa è una rassegna di alcuni risultati recenti sui moltiplicatori spettrali dell'operatore di Ornstein-Uhlenbeck, un laplaciano naturale sullo spazio euclideo munito della misura gaussiana. I risultati sono inquadrati nell'ambito della teoria generale dei moltiplicatori spettrali per laplaciani generalizzati.

Multiple solutions for nonlinear discontinuous elliptic problems near resonance

Nikolaos Kourogenis, Nikolaos Papageorgiou (1999)

Colloquium Mathematicae

We consider a quasilinear elliptic eigenvalue problem with a discontinuous right hand side. To be able to have an existence theory, we pass to a multivalued problem (elliptic inclusion). Using a variational approach based on the critical point theory for locally Lipschitz functions, we show that we have at least three nontrivial solutions when λ λ 1 from the left, λ 1 being the principal eigenvalue of the p-Laplacian with the Dirichlet boundary conditions.

Multiplicity bounds for Steklov eigenvalues on Riemannian surfaces

Mikhail Karpukhin, Gerasim Kokarev, Iosif Polterovich (2014)

Annales de l’institut Fourier

We prove two explicit bounds for the multiplicities of Steklov eigenvalues σ k on compact surfaces with boundary. One of the bounds depends only on the genus of a surface and the index k of an eigenvalue, while the other depends as well on the number of boundary components. We also show that on any given Riemannian surface with smooth boundary the multiplicities of Steklov eigenvalues σ k are uniformly bounded in k .

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