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

作者：Lierl Janna; Sturm Karl Theodor^*

来源：Calculus of Variations and Partial Differential Equations, 2018, 57(1): 25.

DOI：10.1007/s00526-017-1292-8

For large classes of non-convex subsets Y in 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.

• 出版日期2018-2