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

Janna Lierl; Karl-Theodor Sturm

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

Functional Analysis 2017-12-21 v2

Authors: Janna Lierl , Karl-Theodor Sturm

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.

Keywords

Neumann heat flow gradient flow Boltzmann entropy non-convex domain metric measure space RCD-space

Cite

@article{arxiv.1704.04164,
  title  = {Neumann heat flow and gradient flow for the entropy on non-convex domains},
  author = {Janna Lierl and Karl-Theodor Sturm},
  journal= {arXiv preprint arXiv:1704.04164},
  year   = {2017}
}

Comments

to appear in Calc.Var.PDE

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

Abstract

Keywords

Cite

Comments

Related papers