Boundary Behavior of the Fast Diffusion Equation
Ying C. Kwong · Transactions of the American Mathematical Society · 1990
The fast diffusion equation $\Delta {\upsilon ^m} = {\upsilon _t}$, $0 < m < 1$, is a degenerate nonlinear parabolic equation of which the existence of a unique continuous weak solution has been established. In this paper we are going to obtain a Lipschitz growth rate of the solution at the boundary of $\Omega$ and estimate that in terms of the various data.