Free boundary regularity for a problem with right hand side

Details Free boundary regularity for a problem with right hand side Free boundary regularity for a problem with right hand side

2009-12-10

arxiv.org/abs/0912.2057v1

Mathematics

Analysis of PDEs

Scientific paper

We consider a one-phase free boundary problem with variable coefficients and
non-zero right hand side. We prove that flat free boundaries are $C^{1,\alpha}$
using a different approach than the classical supconvolution method of
Caffarelli. We use this result to obtain that Lipschitz free boundaries are
$C^{1,\alpha}$.

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