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Free boundary regularity for a problem with right hand side

Published 2009-12-10Version 1

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 $C^{1,\alpha}$.

Categories: math.AP

Subjects: 35B65

Keywords: free boundary regularity, non-zero right hand side, one-phase free boundary problem, flat free boundaries, lipschitz free boundaries

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