Abstract

We prove local Lipschitz regularity and non-degeneracy estimates for viscosity solutions to one-phase free boundary problems governed by non-homogeneous fully non-linear equations with unbounded ingredients and quadratic growth in the gradient. We use the approach in De Silva (Interfaces Free Bound 13:223–238, 2011) to show that flat or Lipschitz free boundaries are graphs \(C^{1, \alpha }\).

中文翻译：

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具有无界成分和梯度二次增长的非齐次完全非线性方程的自由边界理论

摘要

我们证明了局部Lipschitz正则性和非简并性估计，用于一相自由边界问题的粘度解，该问题由具有成分不受约束的非均匀完全非线性方程和梯度的二次增长控制。我们使用德席尔瓦（接口不含结合13：223-238，该方法2011）表明，扁平或李氏自由的边界是图\（C ^ {1，\阿尔法} \） 。