On the Equality of Solutions of Max-Min and Min-Max Systems of   Variational Inequalities with Interconnected Bilateral Obstacles
  In this paper, we deal with the solutions of systems of PDEs with bilateral inter-connected obstacles of min-max and max-min types. These systems arise naturally in stochastic switching zero-sum game problems. We show that when the switching costs of one side are regular, the solutions of the min-max and max-min systems coincide. Then, this common viscosity solution is related to a multi-dimensional doubly reflected BSDE with bilateral interconnected obstacles. Finally, its relationship with the the values of a zero-sum switching game is studied. 
Boualem Djehiche, Said Hamad\`ene, Marie-Am\'elie Morlais, Xuzhe Zhao
math.PR