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On existence and uniqueness of solutions of Hamilton-Jacobi equations. (English) Zbl 0603.35016
Aus dem Vorwort der Verff: Our main purpose is to establish some uniqueness and existence theorems for Hamilton-Jacobi equations. We will focus on the Cauchy problem \[ u_ t+H(x,t,u,Du)=0\quad in\quad {\mathbb{R}}^ N\times (0,T),\quad u(x,0)=\phi (x), \] and the stationary problem \(u+H(x,u,Du)=0\) in \({\mathbb{R}}^ N\), in which H is a real-valued function of its arguments, x denotes points on \({\mathbb{R}}^ N\), Du stands for the spatial gradient \((u_{x1},...,u_{xN})\) of u, which is itself a real-valued function of either (x,t) or x as appropriate.
Reviewer: J.Wloka

MSC:
35G25 Initial value problems for nonlinear higher-order PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35B50 Maximum principles in context of PDEs
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References:
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