A new regularity estimate for solutions of singular parabolic equations
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.
Received: September 2004; Revised: February 2005; Published: September 2005. |