Vol. 1, No. 2, 2019

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About small eigenvalues of the Witten Laplacian

Laurent Michel

Vol. 1 (2019), No. 2, 149–206
Abstract

We study the low-lying eigenvalues of the semiclassical Witten Laplacian associated to a Morse function ϕ. Compared to previous works we allow general distributions of critical values of ϕ, for instance allowing all the local minima to be absolute. The motivation comes from metastable dynamics described by the Kramers–Smoluchowski equation.

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Keywords
metastability, semiclassical analysis
Mathematical Subject Classification 2010
Primary: 35P20
Milestones
Received: 31 March 2018
Revised: 4 February 2019
Accepted: 6 March 2019
Published: 20 April 2019
Authors
Laurent Michel
Université de Bordeaux
Institut Mathématiques de Bordeaux
Talence
France