Free boundary regularity for a problem with right hand side (Q633939)

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