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Perron’s method for Hamilton-Jacobi equations. (English) Zbl 0697.35030
In order to prove the existence of global weak solutions of the first order nonlinear scalar Hamilton-Jacobi equations \[ (1)\quad F(x,u,Du)=0\quad in\quad \Omega \subset {\mathbb{R}}^ n, \] the author presents a new simple direct method called Perron’s method. This is an analogue for (1) to the well-known method of finding solutions of Laplace equation due to O. Perron [Eine neue Behandlung der ersten Randwertaufgabe für \(\Delta u=0\), Math. Z. 18, 42-54 (1923)].
Reviewer: J.-H.Tian

MSC:
35F30 Boundary value problems for nonlinear first-order PDEs
70H20 Hamilton-Jacobi equations in mechanics
35B50 Maximum principles in context of PDEs
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