2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120080We prove an a-priori bound for the Lipschitz constant of a smooth one-phase free boundary graph F(u) in two dimensions. The function u satisfies a fully nonlinear elliptic equation in its positive side, and the gradient of u is equal to 1 on F(u).16 pagesAnalysis of PDEs35B45text