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• W2892362169 abstract "We introduce the transportation-annihilation distance $W_p^sharp$ between subprobabilities and derive contraction estimates with respect to this distance for the heat flow with homogeneous Dirichlet boundary conditions on an open set in a metric measure space. We also deduce the Bochner inequality for the Dirichlet Laplacian as well as gradient estimates for the associated Dirichlet heat flow. For the Dirichlet heat flow, moreover, we establish a gradient flow interpretation within a suitable space of charged probabilities. In order to prove this, we will work with the emph{doubling} of the open set, the space obtained by gluing together two copies of it along the boundary." @default.
• W2892362169 created "2018-09-27" @default.
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• W2892362169 date "2018-09-04" @default.
• W2892362169 modified "2023-09-27" @default.
• W2892362169 title "Heat Flow with Dirichlet Boundary Conditions via Optimal Transport and Gluing of Metric Measure Spaces" @default.
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