论文标题
完全非线性的无线性传输问题
A fully nonlinear free transmission problem
论文作者
论文摘要
我们检查了由完全非线性椭圆运算符驱动的自由传输问题。由于透射界面是内差确定的，因此我们的分析是两个方面：我们研究溶液的规律性和自由边界的某些几何特性。通过将我们的问题与一对粘度不平等联系起来，我们证明了强大的解决方案是本地$ c ^{1,1} $的类。至于自由边界，我们首先建立薄弱的结果，例如其非分类，然后继续进行全球解决方案的表征。
We examine a free transmission problem driven by fully nonlinear elliptic operators. Since the transmission interface is determined endogeneously, our analysis is two-fold: we study the regularity of the solutions and some geometric properties of the free boundary. By relating our problem with a pair of viscosity inequalities, we prove that strong solutions are of class $C ^{1,1}$, locally. As regards the free boundary, we start by establishing weak results, such as its non-degeneracy, and proceed with the characterization of global solutions.
