A System of Nonlinear Partial Differential Equations Arising in the Optimal Control of Stochastic Systems with Switching Costs
Suzanne Lenhart, Stavros A. Belbas · SIAM Journal on Applied Mathematics · 1983
The problem of optimal switching control of a diffusion process with costly switchings leads to a system of fully nonlinear elliptic partial differential equations with implicit obstacles. We obtain results on the existence, uniqueness and regularity of the solution of this system.