Global positivity estimates and Harnack inequalities for the fast diffusion equation |
| |
Authors: | Matteo Bonforte Juan Luis Vazquez |
| |
Institution: | aDepartamento de Matemáticas, Universidad Autónoma de Madrid, Campus de Cantoblanco, 28049 Madrid, Spain;bDipartimento di Matematica, Politecnico di Torino, corso Duca degli Abruzzi 24, 10129 Torino, Italy |
| |
Abstract: | We investigate local and global properties of positive solutions to the fast diffusion equation ut=Δum in the range (d−2)+/d<m<1, corresponding to general nonnegative initial data. For the Cauchy problem posed in the whole Euclidean space we prove sharp local positivity estimates (weak Harnack inequalities) and elliptic Harnack inequalities; we use them to derive sharp global positivity estimates and a global Harnack principle. For the mixed initial and boundary value problem posed in a bounded domain of with homogeneous Dirichlet condition, we prove weak and elliptic Harnack inequalities. Our work shows that these fast diffusion flows have regularity properties comparable and in some senses better than the linear heat flow. |
| |
Keywords: | Nonlinear evolutions Fast diffusion Harnack inequalities Positivity Asymptotics |
本文献已被 ScienceDirect 等数据库收录! |
|