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arXiv · 1704.04164

Neumann heat flow and gradient flow for the entropy on non-convex domains

Janna Lierl·Karl-Theodor Sturm
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Abstract

For large classes of non-convex subsets $Y$ in ${\mathbb R}^n$ or in Riemannian manifolds $(M,g)$ or in RCD-spaces $(X,d,m)$ we prove that the gradient flow for the Boltzmann entropy on the restricted metric measure space $(Y,d_Y,m_Y)$ exists - despite the fact that the entropy is not semiconvex - and coincides with the heat flow on $Y$ with Neumann boundary conditions.

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Janna Lierl, Karl-Theodor Sturm. 2017-04-13. Neumann heat flow and gradient flow for the entropy on non-convex domains. https://arxiv.org/abs/1704.04164

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