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Displaying similar documents to “Metric properties of eigenfunctions of the Laplace operator on manifolds”

Harnack inequalities on a manifold with positive or negative Ricci curvature.

Dominique Bakry, Zhongmin M. Qian (1999)

Revista Matemática Iberoamericana

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Several new Harnack estimates for positive solutions of the heat equation on a complete Riemannian manifold with Ricci curvature bounded below by a positive (or a negative) constant are established. These estimates are sharp both for small time, for large time and for large distance, and lead to new estimates for the heat kernel of a manifold with Ricci curvature bounded below.

An inverse problem for the equation u = - c u - d

Michael Vogelius (1994)

Annales de l'institut Fourier

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Let Ω be a bounded, convex planar domain whose boundary has a not too degenerate curvature. In this paper we provide partial answers to an identification question associated with the boundary value problem u = - c u - d in Ω , u = 0 on Ω . We prove two results: 1) If Ω is not a ball and if one considers only solutions with - c u - d 0 , then there exist at most finitely many pairs of coefficients ( c , d ) so that the normal derivative u ν | Ω equals a given ψ 0 . 2) If one imposes no sign condition on the...