Hardy inequality and heat semigroup estimates for Riemannian manifolds with singular data - Mathematics > Spectral TheoryReport as inadecuate




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Abstract: Upper bounds are obtained for the heat content of an open set D in ageodesically complete Riemannian manifold M with Dirichlet boundary conditionon bdD, and non-negative initial condition. We show that these upper boundsare close to being sharp if i the Dirichlet-Laplace-Beltrami operator actingin $L^2D$ satisfies a strong Hardy inequality with weight $r^2$, ii theinitial temperature distribution, and the specific heat of D are given by$r^{-a}$ and $r^{-b}$ respectively, where $r$ is the distance to the boundary,and 1


Author: M. van den Berg, P. Gilkey, K. Kirsten, A. Grigor'yan

Source: https://arxiv.org/







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