论文标题
Picard-Lindelöf定理，用于平滑PDE
A Picard-Lindelöf theorem for smooth PDE
论文作者
论文摘要
我们证明，如果我们假设合适的Weissinger样足够的条件，则Picard-lindelöf迭代为PDE的任意平滑正常cauchy问题，以融合PDE。该条件既包括一类非分析的PDE或初始条件，也包括更经典的实际分析功能。该证明是基于Banach固定点定理，用于收缩和衍生物的损失。从后者中，我们还证明了局部Lipschitz地图的逆函数定理，并在任意分级的Fréchet空间中衍生物丢失。
We prove that Picard-Lindelöf iterations for an arbitrary smooth normal Cauchy problem for PDE converge if we assume a suitable Weissinger-like sufficient condition. This condition includes both a large class of non-analytic PDE or initial conditions, and more classical real analytic functions. The proof is based on a Banach fixed point theorem for contractions with loss of derivatives. From the latter, we also prove an inverse function theorem for locally Lipschitz maps with loss of derivatives in arbitrary graded Fréchet spaces.
