Higher regularity estimates for the porous medium equation near the heat equation
Higher regularity estimates for the porous medium equation near the heat equation
In this paper we investigate regularity aspects for solutions of the nonlinear parabolic equation u_t= \Delta u^m, \quad m > 1, usually called the porous medium equation. More precisely, we provide sharp regularity estimates for bounded nonnegative weak solutions along the free boundary \partial\{u > 0\} , when the equation …