The singular homogeneous solutions to one phase free boundary problem

Hong, Guanghao

doi:10.1090/S0002-9939-2015-12553-1

The singular homogeneous solutions to one phase free boundary problem
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by Guanghao Hong PDF

Proc. Amer. Math. Soc. 143 (2015), 4009-4015 Request permission

Abstract:

We provide some new examples of singular homogeneous of degree one solutions to the well-known one phase free boundary problem. They are critical points of the functional $J(v,B)=\int _B |\nabla v|^2+\chi _{\{v>0\}}$. We also discuss their stability using a criteria of Caffarelli, Jerison and Kenig.

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