Damião J. Araújo
In this paper we investigate regularity aspects for solutions of the nonlinear parabolic equation ut=Δum,m>1, usually called the porous medium equation. More precisely, we provide sharp regularity estimates for bounded nonnegative weak solutions along the free boundary ∂{u>0}, when the equation is universally close to the heat equation. As a consequence, local Lipschitz estimates are also established for this scenario.
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