Viscosity solutions of systems of PDEs with interconnected obstacles and   Multi modes switching problems
  This paper deals with existence and uniqueness, in viscosity sense, of a solution for a system of m variational partial differential inequalities with inter-connected obstacles. A particular case of this system is the deterministic version of the Verification Theorem of the Markovian optimal m-states switching problem. The switching cost functions are arbitrary. This problem is connected with the valuation of a power plant in the energy market. The main tool is the notion of systems of reflected BSDEs with oblique reflection. 
Said Hamad\`ene, Marie-Am\'elie Morlais
math.OC cs.SY