We consider a one-phase free boundary problem with variable coefficients and nonzero right hand side. We prove that flat free boundaries are _C_1, using a different approach than the classical supconvolution method of Caffarelli. We use this result to deduce that Lipschitz free boundaries are _C_1,.
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Daniela De Silva, Free boundary regularity for a problem with right hand side. Interfaces Free Bound. 13 (2011), no. 2, pp. 223–238DOI 10.4171/IFB/255