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September, 2011 Nonnegative solutions of the heat equation on rotationally symmetric Riemannian manifolds and semismall perturbations
Minoru Murata
Rev. Mat. Iberoamericana 27(3): 885-907 (September, 2011).

Abstract

Let $M$ be a rotationally symmetric Riemannian manifold, and $\Delta$ be the Laplace-Beltrami operator on $M$. We establish a necessary and sufficient condition for the constant function 1 to be a semismall perturbation of $-\Delta +1$ on $M$, and give optimal sufficient conditions for uniqueness of nonnegative solutions of the Cauchy problem to the heat equation. As an application, we determine the structure of all nonnegative solutions to the heat equation on $M\times(0,T)$.

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Minoru Murata . "Nonnegative solutions of the heat equation on rotationally symmetric Riemannian manifolds and semismall perturbations." Rev. Mat. Iberoamericana 27 (3) 885 - 907, September, 2011.

Information

Published: September, 2011
First available in Project Euclid: 9 August 2011

zbMATH: 1227.58007
MathSciNet: MR2895337

Subjects:
Primary: 31C12 , 31C35 , 35B20 , 35C15 , 35J99 , 35K05 , 35K15 , 58J99

Keywords: heat equation , integral representation , Laplace operator , Martin boundary , nonnegative solution , rotationally symmetric Riemannian manifold , semismall perturbation , uniqueness

Rights: Copyright © 2011 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.27 • No. 3 • September, 2011
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