We use non-variational type arguments to prove optimal regularity and smoothness of the free boundary for one-phase solutions to inhomogeneous nonlinear free boundary problems (FBP) governed by singular/degenerate elliptic PDEs with a nonzero right hand side (RHS). In a precise way, we show that viscosity solutions to FBP, as previously mentioned, are locally Lipschitz continuous and under certain conditions, flat or Lipschitz free boundaries, are \(C^{1, \alpha }.\)

中文翻译：

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带有右手边的奇异/退化非线性方程的自由边界理论：一种无变量方法

我们使用非变量类型参数来证明自由边界的最佳规则性和光滑度，用于一阶解的非均质非线性自由边界问题（FBP），该问题由具有非零右手边（RHS）的奇异/退化椭圆PDE决定。以一种精确的方式，我们证明，如前所述，FBP的粘度溶液是局部Lipschitz连续的，在某些条件下，平坦或Lipschitz自由边界为\（C ^ {1，\ alpha}。\）