IPM Calendar 
Thursday 18 July 2019   Today  
Events for day: Wednesday 13 February 2019    
           15:30 - 17:00     Geometry and Topology Weekly Seminar
Non-strictly Convex Gradient Constraints in Calculus of Variations


We prove the optimal regularity for variational problems with convex gradient constraints. We do not assume any regularity of the constraints; so the constraints can be non-smooth, and they need not be strictly convex. When the domain is smooth enough, we show that the optimal regularity holds up to the boundary. In this process, we also characterize the set of singular points of the viscosity solutions to some Hamilton-Jacobi equations. Furthermore, we obtain an explicit formula for the second derivative of these viscosity solutions; and we show that the second derivatives satisfy a monotonicity property. ...