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

$ \begin{equation*} \left\{ \begin{array}{rcll} |D u|^\gamma F(x, D^2u)& = & f(x)\chi_{\{u>\phi\}} & \ \rm{ in } \ B_1 \\ u(x) & \geq & \phi(x) & \ \rm{ in } \ B_1 \\ u(x) & = & g(x) & \ \rm{on } \ \partial B_1, \end{array} \right. \end{equation*} $

中文翻译：

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退化的障碍物类型问题的清晰规律性：一种几何方法

我们证明了由一类退化的完全非线性算子驱动的障碍物类型问题的解的精确规律估计。更具体地说，我们考虑

$ \ begin {equation *} \ left \ {\ begin {array} {rcll} | D u | ^ \ gamma F（x，D ^ 2u）＆=＆f（x）\ chi _ {\ {u> \ phi \}}＆\ \ rm {in} \ B_1 \\ u（x）＆\ geq＆\ phi（x）＆\ \ rm {in} \ B_1 \\ u（x）＆=＆g（x）＆ \ \ rm {on} \ \ partial B_1，\ end {array} \ right。\ end {equation *} $