Neumann heat flow and gradient flow for the entropy on non-convex domains
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Publication:6285481
DOI10.1007/S00526-017-1292-8zbMath1516.35014arXiv1704.04164MaRDI QIDQ6285481
Janna Lierl, Karl-Theodor Sturm
Publication date: 13 April 2017
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.
Initial-boundary value problems for second-order parabolic equations (35K20) Variational methods applied to PDEs (35A15) Heat and other parabolic equation methods for PDEs on manifolds (58J35)
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