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

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 نشر من قبل Karl-Theodor Sturm
 تاريخ النشر 2017
  مجال البحث
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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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