Free boundary regularity for a problem with right hand side

Abstract

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 $C^{1,\alpha }$.

References in corpus (1)

• A geometric approach to generalized Stokes conjectures