Optimal decay rate for degenerate parabolic equations on noncompact manifolds (Q259616)

The authors consider an initial value problem for a doubly degenerate parabolic equation in a noncompact Riemannian manifold. They prove optimal \(L^1\)-\(L^{\infty}\) estimates. They introduce a simplified version of the by now classical local approach by De Giorgi, Ladyzhenskaya-Ural'tseva, and DiBenedetto, which is of great and independent interest even in the Euclidean case. In the Riemannian setting, the authors discriminate between manifolds satisfying a Faber-Krahn inequality or a relative Faber-Krahn inequality.