Multiplicative Functional for the Heat Equation on Manifolds with Boundary
The multiplicative functional for the heat equation on k-forms with absolute boundary condition is constructed and a probabilistic representation of the solution is obtained. As an application, we prove a heat kernel domination that was previously discussed by Donnelly and Li, and Shigekawa.
KeywordsAbsolute boundary condition Gradient inequality Heat kernel domination Hodge-de Rham Laplacian Riemannian manifold with boundary
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