Minimax solutions of Hamilton-Jacobi equation (Q2771545)

This paper deals with different concepts of solution of the partial differential equation NEWLINE\[NEWLINEF(x,u(x),Du(x))=0,\quad x\in G\subset R^{n},NEWLINE\]NEWLINE where \(G\) is an open set in \(R^{n}\); \(Du=(\partial u/\partial x_1,\ldots,\partial u/\partial x_{n})\). The author gives different definitions of a generalized (in minimax sense) solution of the considered equation and studies relations of these notions and notions of upper, lower solutions, and viscosity solutions. A survey of results obtained by the author in the theory of minimax solutions is presented.NEWLINENEWLINEFor the entire collection see [Zbl 0949.00042].