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 $C^{1,\alpha}$ 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2018
- DOI:
- 10.48550/arXiv.1812.08770
- arXiv:
- arXiv:1812.08770
- Bibcode:
- 2018arXiv181208770K
- Keywords:
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- Mathematics - Analysis of PDEs;
- 35R35;
- 35K65;
- 35A21
- E-Print:
- 39 pages, 1 figure