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

2017/04/13 by Lierl, Janna, Sturm, Karl-Theodor
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1704.04164

Abstract

For large classes of non-convex subsets Y in \mathbb Rⁿ 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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