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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.17543 |
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Table of Contents:
- We prove a quantitative inhomogeneous Hopf-Oleinik lemma for viscosity solutions of $$|\nabla u|^αF(D^{2}u)=f $$ and, more generally, for viscosity supersolutions of $|\nabla u|^α\,{M}^-_{λ,Λ}(D^{2}u)\le f$. The result yields linear boundary growth with universal constants depending only on the structural data. We also exhibit a counterexample showing that the Hopf lemma fails for equations that act only in the large-gradient regime (in the sense of Imbert and Silvestre), thereby delineating the scope of our theorem. 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 $\varepsilon$-uniform Lipschitz bounds for a one-phase flame propagation model.