## Regularity of the free boundary for the porous medium equation

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- by P. Daskalopoulos and R. Hamilton PDF
- J. Amer. Math. Soc.
**11**(1998), 899-965 Request permission

## Abstract:

We study the regularity of the free boundary for solutions of the porous medium equation $u_{t}=\Delta u^{m}$, $m >1$, on ${\mathcal {R}}^{2} \times [0,T]$, with initial data $u^{0}=u(x,0)$ nonnegative and compactly supported. We show that, under certain assumptions on the initial data $u^{0}$, the pressure $f=m u^{m-1}$ will be smooth up to the interface $\Gamma = \partial \{ u >0 \}$, when $0<t\leq T$, for some $T >0$. As a consequence, the free-boundary $\Gamma$ is smooth.## References

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## Additional Information

**P. Daskalopoulos**- Affiliation: Department of Mathematics, University of California, Irvine, California 92697-3875
- MR Author ID: 353551
- Email: pdaskalo@math.uci.edu
**R. Hamilton**- Affiliation: Department of Mathematics, University of California at San Diego, La Jolla, California 92093-0001
- Received by editor(s): January 19, 1998
- © Copyright 1998 American Mathematical Society
- 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