Almost minimizers of the one-phase free boundary problem. Issue 8 (2nd August 2020) - De Silva, D.; Savin, O.
Abstract: We consider almost minimizers to the one-phase energy functional and we prove their optimal Lipschitz regularity and partial regularity of their free boundary. These results were recently obtained by David and Toro, and David, Engelstein, and Toro. Our proofs provide a different method based on a non-infinitesimal notion of viscosity solutions that we introduced.