论文标题
部分可观测时空混沌系统的无模型预测
Continuity of infinitely degenerate weak solutions via the trace method
论文作者
论文摘要
1971年，联邦（Fedi）证明了一个显着的定理，即具有系数1和f^2的平面线性二阶偏差算子，只要F平滑，原点就消失了，否则为正。作者最近给出了该结果的变异，并由弱解决方案的连续性取代，以及Cristian Rios和Ruipeng Shen，以无限退化的椭圆形差异形式方程式，其中非阴性矩阵A（x，X，U）具有可测量的iSNISTIBLABL -LOBLABL -1和FRACE IS依赖性（frable 1 and N），并确定f）（f），而F）则是F）。加倍。但是，在平面上，这些变体在F上假定了其他几何约束，这在Fediĭ定理中不需要。在本文中，我们尤其在平面上删除了这些额外的几何约束，以使F基本上翻倍。
In 1971 Fediĭ proved the remarkable theorem that the linear second order partial differential operator in the plane with coefficients 1 and f^2 is hypoelliptic provided that f is smooth, vanishes at the origin and is positive otherwise. Variants of this result, with hypoellipticity replaced by continuity of weak solutions, were recently given by the authors, together with Cristian Rios and Ruipeng Shen, to infinitely degenerate elliptic divergence form equations where the nonnegative matrix A(x,u) has bounded measurable coefficients with trace roughly 1 and determinant comparable to f, and where F=ln(1/f) is essentially doubling. However, in the plane, these variants assumed additional geometric constraints on f, something not required in Fediĭ's theorem. In this paper we in particular remove these additional geometric constraints in the plane for homogeneous equations with F essentially doubling.
