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- W2986943902 abstract "We prove sharp regularity estimates for solutions of obstacle type problems driven by a class of degenerate fully nonlinear operators; more specifically, we consider viscosity solutions of [ |D u|^gamma F(x, D^2u) = f(x)chi_{{u>phi}} textrm{ in } B_1 ] with $gamma>0$, $phi in C^{1, alpha}(B_1)$ for some $alphain(0,1]$ and $fin L^infty(B_1)$ constrained to satisfy [ ugeq phitextrm{ in } B_1 ] and prove that they are $C^{1,beta}(B_{1/2})$ (and in particular along free boundary points) where $beta=minleft{alpha, frac{1}{gamma+1}right}$. Moreover, we achieve such a feature by using a recently developed geometric approach which is a novelty for these kind of free boundary problems. Further, under a natural non-degeneracy assumption on the obstacle, we prove that the free boundary $partial{u>phi}$ has zero Lebesgue measure. Our results are new even for seemingly simple model as follows [ |Du|^gamma Delta u=chi_{{u>phi}} quad text{with}quad gamma>0. ]" @default.
- W2986943902 created "2019-11-22" @default.
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- W2986943902 date "2019-11-01" @default.
- W2986943902 modified "2023-09-27" @default.
- W2986943902 title "Sharp regularity for degenerate obstacle type problems: a geometric approach." @default.
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