A Quantitative Hopf-Oleinik Lemma for Degenerate Fully Nonlinear Operators and Applications to Free Boundary Problems
Year: 2026
Type: article
Abstract: We prove a quantitative inhomogeneous Hopf-Oleinik lemma for viscosity solutions of $$ |\nabla u|^{\alpha }F(D^{2}u)=f $$ | ∇ u | α F ( D 2 u ) = f and, more generally, for viscosity supersolutions of $$|\nabla u|^{\alpha }\,\mathcal {M}^{-}_{\lambda ,\Lambda }(D^{2}u)\le f$$ | ∇ u | α M λ , Λ - ( D 2 u ) ≤ 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 $$\varepsilon $$ ε –uniform Lipschitz bounds for a one–phase flame propagation model.
Source: La Matematica
Institutions: University of Bologna, Universidade Federal do Ceará
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W7136148594