论文标题
完全非线性退化的免费传输问题
A fully nonlinear degenerate free transmission problem
论文作者
论文摘要
我们研究了由退化的完全非线性操作员驱动的自由传输问题。我们的第一个结果涉及有关相关的Dirichlet问题的解决方案。通过在粘度不平等的背景下构建方程，我们为粘度解决方案和某些强大的解决方案产生最佳的规律性结果。我们的发现包括$ c^{1，α} $空间中的规律性，以及在退化率方面的明确表征$α$。我们通过扰动方法来争论，将我们的问题与均匀的，完全非线性均匀的椭圆方程联系起来。
We study a free transmission problem driven by degenerate fully nonlinear operators. Our first result concerns the existence of solutions to the associated Dirichlet problem. By framing the equation in the context of viscosity inequalities, we produce optimal regularity results for viscosity solutions and certain strong solutions to the problem. Our findings include regularity in $ C^{1,α}$ spaces, and an explicit characterization of $α$ in terms of the degeneracy rates. We argue by perturbation methods, relating our problem to a homogeneous, fully nonlinear uniformly elliptic equation.
