Regularity of the free boundary

for the porous medium equation

Authors:
P. Daskalopoulos and R. Hamilton

Journal:
J. Amer. Math. Soc. **11** (1998), 899-965

MSC (1991):
Primary 35Jxx

DOI:
https://doi.org/10.1090/S0894-0347-98-00277-X

MathSciNet review:
1623198

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Abstract | References | Similar Articles | Additional Information

Abstract: We study the regularity of the free boundary for solutions of the porous medium equation , , on , with initial data nonnegative and compactly supported. We show that, under certain assumptions on the initial data , the pressure will be smooth up to the interface , when , for some . As a consequence, the free-boundary is smooth.

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Additional Information

**P. Daskalopoulos**

Affiliation:
Department of Mathematics, University of California, Irvine, California 92697-3875

Email:
pdaskalo@math.uci.edu

**R. Hamilton**

Affiliation:
Department of Mathematics, University of California at San Diego, La Jolla, California 92093-0001

DOI:
https://doi.org/10.1090/S0894-0347-98-00277-X

Keywords:
Porous medium equation,
free-boundary,
$C^{\infty }$-regularity

Received by editor(s):
January 19, 1998

Article copyright:
© Copyright 1998
American Mathematical Society