The Journal of Geometric Analysis

, Volume 15, Issue 4, pp 641-667

First online:

The one-phase Hele-Shaw problem with singularities

  • David JerisonAffiliated withDepartment of Mathematics, MIT Email author 
  • , Inwon KimAffiliated withDepartment of Mathematics, UCLA

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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.

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Key Words and Phrases

Free boundary singularity analysis viscosity solutions Hele-Shaw flow