
Geometry and Topology Weekly Seminar

سمینار هفتگی هندسه و توپولوژی




TITLE

Nonstrictly Convex Gradient Constraints in Calculus of Variations



SPEAKER

Mohammad Safdari



Sharif University of Technology







TIME

Wednesday, February 13, 2019,


15:30  17:00




VENUE 
Lecture Hall 1, Niavaran Bldg.



SUMMARY 


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 nonsmooth, 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 HamiltonJacobi 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.




تهران، ضلع جنوبی
ميدان شهيد باهنر (نياوران)، پژوهشگاه
دانشهای بنيادی، پژوهشکده رياضيات
School of
Mathematics, Institute for Research in
Fundamental Sciences (IPM), Niavaran
Bldg., Niavaran Square, Tehran
ipmmath@ipm.ir
♦ +98 21
22290928 ♦
math.ipm.ir 


