Communications in Analysis and Geometry

Volume 12 (2004)

Number 1

Geometric Estimates for the Logarithmic Fast Diffusion Equation

Pages: 143 – 164

DOI: http://dx.doi.org/10.4310/CAG.2004.v12.n1.a8

Authors

P. Daskalopoulos

R. Hamilton

Abstract

We consider solutions u of the logarithmic fast diffusion equation {δu \over δt } = ϔlogu (1.1) on the plane R2, with initial data f ≥ 0 of finite mass. ϔ denotes the Euclidean Laplace operator

ϔ = δ2 δx2 + δ2 δy2

with respect to the standard metric ds2 = dx2+dy2.

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