Third boundary value problem for the heat equation. I.
Miroslav Dont (1981)
Časopis pro pěstování matematiky
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Miroslav Dont (1981)
Časopis pro pěstování matematiky
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Michele Miranda, Diego Pallara, Fabio Paronetto, Marc Preunkert (2007)
Annales de la faculté des sciences de Toulouse Mathématiques
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We prove a characterisation of sets with finite perimeter and functions in terms of the short time behaviour of the heat semigroup in . For sets with smooth boundary a more precise result is shown.
Lucio Berrone, Paola Mannucci (2004)
Control and Cybernetics
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Briozzo, Adriana C., Tarzia, Domingo A. (2006)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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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.