Perron's method for Hamilton-Jacobi equations (Q910925)

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 \textit{O. Perron} [Eine neue Behandlung der ersten Randwertaufgabe für \(\Delta u=0\), Math. Z. 18, 42-54 (1923)].