MR2867013 Sunao ŌUCHI Sunao ŌUCHI Existence of Classical Solutions near Characteristic Points of First Order Nonlinear Partial Differential Equations Funkcialaj Ekvacioj. Serio Internacia 54 2011 177--224 http://fe.math.kobe-u.ac.jp/FE/FullPapers/54-2/54_177.pdf http://www.ams.org/mathscinet-getitem?mr=MR2867013 We treat a nonlinear partial differential equation $F(x,u,u_x)=0$ in a neighborhood of $x=0 \in \mathbb{R}^d$, where $F(x,u,p)$ is a real-valued smooth function. It is well-known that solutions are constructed by solving noncharacteristic Cauchy problem with the method of characteristics, provided $F_{p_i}(0,0,0)\not=0$ for some $i$. In this paper we study the existence of a classical solution under the condition that $F_{p_i}(0,0,0)=0$ for all $1\leq i \leq d$. First order singular nonlinear partial differential equations. Primary 35F20, Secondary 35A01, 35A09. 54-177 2011 Existence of Classical Solutions near Characteristic Points of First Order Nonlinear Partial Differential Equations Sunao ŌUCHI Sunao ŌUCHI
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