DIFFERENTIAL GAME WITH SWITCHING CONTROLS ON HILBERT-SPACE

We study differential game problems in which the players can select di fferent maximal monotone operators for the governing evolution system. Setting up our problem on a real Hilbert space, we show that the Elli ott-Kalton upper and lower value of the game are viscosity solution of some Hamilton-Jacobi-Isaacs equations. Uniqueness is obtained by assu ming condition analogous to the classical Isaacs condition, and thus t he existence of value of the game follows.