Abstract We prove a quantitative inhomogeneous Hopf-Oleinik lemma for viscosity solutions of | u|^ F (D^2u) =f | ∇ u | α F (D 2 u) = f and, more generally, for viscosity supersolutions of | u|^ \, M^-, (D^2u) 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 ε –uniform Lipschitz bounds for a one–phase flame propagation model.
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Davide Giovagnoli
University of Bologna
Enzo Maria Merlino
University of Bologna
Diego Moreira
La Matematica
University of Bologna
Universidade Federal do Ceará
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Giovagnoli et al. (Mon,) studied this question.
synapsesocial.com/papers/69ba422e4e9516ffd37a22fb — DOI: https://doi.org/10.1007/s44007-026-00201-4
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