On manimax theory in two Hilbert spaces

Abstract

In this paper, we investigated the minimax of the bifunction J:H1(Ω)xV2→RmxRn, such that J(v1,v2)=((12a(v1,v1)−L(v1)),v2) where a(.,.) is a finite symmetric bilinear bicontinuous, coercive form on H1(Ω) and L belongs to the dual of H1(Ω).In order to obtain the minimax point we use lagrangian functional.