Abstract: In this work we discuss the limits of direct methods for Optimal Control Problems (OCPs) for some classes of nonsmooth dynamic systems. We highlight the equivalence between Filippov systems ...

Abstract: Boundary value problems involving elliptic PDEs such as the Laplace and the Helmholtz equations are ubiquitous in mathematical physics and engineering. Many such problems can be ...

Mathematicians finally understand the behavior of an important class of differential equations that describe everything from water pressure to oxygen levels in human tissues. The trajectory of a storm ...