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A new regularity estimate for solutions of singular parabolic equations

Pages: 605 - 610, Issue Special, August 2005

 Abstract        Full Text (193.2K)              

Gary Lieberman - Department of Mathematics, Iowa State University, Ames, IA 50011, United States (email)

Abstract: 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, regularity of solutions, initial conditions, a priori estimates.
Mathematics Subject Classification:  Primary: 35K15, 35B65; Secondary: 35K55, 35B45.

Received: September 2004;      Revised: February 2005;      Published: September 2005.