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The one-phase Hele-Shaw problem with singularities

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Abstract

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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Authors and Affiliations

  1. Department of Mathematics, MIT, USA

    David Jerison

  2. Department of Mathematics, UCLA, USA

    Inwon Kim

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  1. David Jerison
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  2. Inwon Kim
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Correspondence to David Jerison.

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Jerison, D., Kim, I. The one-phase Hele-Shaw problem with singularities. J Geom Anal 15, 641–667 (2005). https://doi.org/10.1007/BF02922248

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  • DOI: https://doi.org/10.1007/BF02922248

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