The lower bound of the Ricci curvature that yields an infinite discrete spectrum of the Laplacian

Hironori Kumura

Displaying similar documents to “The lower bound of the Ricci curvature that yields an infinite discrete spectrum of the Laplacian”

Accurate eigenvalue asymptotics for the magnetic Neumann Laplacian

Soeren Fournais, Bernard Helffer (2006)

Annales de l’institut Fourier

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Motivated by the theory of superconductivity and more precisely by the problem of the onset of superconductivity in dimension two, many papers devoted to the analysis in a semi-classical regime of the lowest eigenvalue of the Schrödinger operator with magnetic field have appeared recently. Here we would like to mention the works by Bernoff-Sternberg, Lu-Pan, Del Pino-Felmer-Sternberg and Helffer-Morame and also Bauman-Phillips-Tang for the case of a disc. In the present paper we settle...

Fokker-Planck equation in bounded domain

Laurent Chupin (2010)

Annales de l’institut Fourier

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We study the existence and the uniqueness of a solution $ϕ$ to the linear Fokker-Planck equation $- Δ ϕ + div (ϕ F) = f$ in a bounded domain of $ℝ^{d}$ when $F$ is a “confinement” vector field. This field acting for instance like the inverse of the distance to the boundary. An illustration of the obtained results is given within the framework of fluid mechanics and polymer flows.