# American Institute of Mathematical Sciences

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

## A new regularity estimate for solutions of singular parabolic equations

 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 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  [1] Dian Palagachev, Lubomira Softova. A priori estimates and precise regularity for parabolic systems with discontinuous data. Discrete & Continuous Dynamical Systems, 2005, 13 (3) : 721-742. doi: 10.3934/dcds.2005.13.721 [2] Xavier Cabré, Manel Sanchón, Joel Spruck. A priori estimates for semistable solutions of semilinear elliptic equations. 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