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2005, 2005(Special): 605-610. doi: 10.3934/proc.2005.2005.605

A new regularity estimate for solutions of singular parabolic equations

Gary Lieberman 1,

1. 

Department of Mathematics, Iowa State University, Ames, IA 50011

Received  September 2004 Revised  February 2005 Published  September 2005

In 1982, K. Ecker showed that solutions of the parabolic equation \[ u_t=\operatorname {div} \left( \frac {Du}{(1+|Du|^2)^{1/2}}\right) + H(x,u) \] have a very unusual regularity property: The interior regularity of $u$ is determined only by its initial regularity. In this note, we show that a similar result is true for a general class of equations. The model equation is \[ u_t=\operatorname {div} \left( |Du|^{p-2} {Du}\right) \] with $1

Keywords: Singular parabolic equations, initial conditions, regularity of solutions, a priori estimates..
Mathematics Subject Classification: Primary: 35K15, 35B65; Secondary: 35K55, 35B4.
Citation: Gary Lieberman. A new regularity estimate for solutions of singular parabolic equations. Conference Publications, 2005, 2005 (Special) : 605-610. doi: 10.3934/proc.2005.2005.605
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