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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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