The one-phase Hele-Shaw problem with singularities
- Cite this article as:
- Jerison, D. & Kim, I. J Geom Anal (2005) 15: 641. doi:10.1007/BF02922248
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In this article we analyze viscosity solutions of the one phase Hele-Shaw problem in the plane and the corresponding free boundaries near a singularity. We find, up to order of magnitude, the speed at which the free boundary moves starting from a wedge, cusp, or finger-type singularity. Maximum principle-type arguments play a key role in the analysis.