Heat flow and Hardy inequality in complete Riemannian manifolds with singular initial conditions |
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Authors: | M. van den Berg |
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Affiliation: | Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom |
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Abstract: | Upper bounds are obtained for the heat content of an open set D with singular initial condition f on a complete Riemannian manifold, provided (i) the Dirichlet-Laplace-Beltrami operator satisfies a strong Hardy inequality, and (ii) f satisfies an integrability condition. Precise asymptotic results for the heat content are obtained for an open bounded and connected set D in Euclidean space with C2 boundary, and with initial condition f(x)=δ(x)−α,0<α<2, where δ(x) is the distance from x to the boundary of D. |
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Keywords: | Riemannian manifold Heat content Hardy inequality |
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