We prove a quantitative inhomogeneous Hopf-Oleinik lemma for viscosity solutions of (Formula presented.) and, more generally, for viscosity supersolutions of |∇u|αMλ,Λ-(D2u)≤f. The result yields linear boundary growth with universal constants depending only on the structural data. As applications, we obtain Lipschitz regularity for viscosity solutions of one–phase Bernoulli free boundary problems driven by these degenerate fully nonlinear operators and derive ε–uniform Lipschitz bounds for a one–phase flame propagation model.
Giovagnoli, D., Merlino, E.M., Moreira, D. (2026). A Quantitative Hopf-Oleinik Lemma for Degenerate Fully Nonlinear Operators and Applications to Free Boundary Problems. LA MATEMATICA, 5(2), 1-43 [10.1007/s44007-026-00201-4].
A Quantitative Hopf-Oleinik Lemma for Degenerate Fully Nonlinear Operators and Applications to Free Boundary Problems
Merlino E. M.;
2026
Abstract
We prove a quantitative inhomogeneous Hopf-Oleinik lemma for viscosity solutions of (Formula presented.) and, more generally, for viscosity supersolutions of |∇u|αMλ,Λ-(D2u)≤f. The result yields linear boundary growth with universal constants depending only on the structural data. As applications, we obtain Lipschitz regularity for viscosity solutions of one–phase Bernoulli free boundary problems driven by these degenerate fully nonlinear operators and derive ε–uniform Lipschitz bounds for a one–phase flame propagation model.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
