Porous Medium Equation with A Drift: Free boundary Regularity
Abstract
We study regularity properties of the free boundary for solutions of the porous medium equation with the presence of drift. We show the C1,α regularity of the free boundary, when the solution is directionally monotone in space variable in a local neighborhood. The main challenge lies in establishing a local non-degeneracy estimate (Theorem 1.3 and Proposition 1.5), which appears new even for the zero drift case.
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