BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Héctor Chang-Lara (CIMAT) DTSTART:20201113T160000Z DTEND:20201113T170000Z DTSTAMP:20260423T041505Z UID:RJWAPDE/17 DESCRIPTION:Title: Eikonal vs. Brownian: Regularity for the solution of an equation with gra dient constraint.\nby Héctor Chang-Lara (CIMAT) as part of Rio de Jan eiro webinar on analysis and partial differential equations\n\n\nAbstract\ nTwo controllers are in charge of steering a spaceship in some domain Omeg a. The first controller wants to spend as much time as possible exploring Omega while the second wants to get out of it as quickly as possible. The first controller determines minute by minute whether the ship is moving by a Brownian motion or with constant speed\, in which case it is the second controller who chooses the direction. Under these instructions\, determin ing the optimal strategies for each player leads us to solve the equation $\\min (-\\Delta u\, |Du|) = 1$ which has several interesting characterist ics. Among them is the presence of a free boundary which separates the reg ions where a Poisson or an Eikonal equation is satisfied. In a recent coll aboration with Edgard Pimentel (PUC-Rio) we showed that the solutions are Lipschitz continuous and that $|Du|$ is continuous\, even though the gradi ent is discontinuous in numerous examples. This problem is a simplificatio n of interesting models in financial mathematics related with the optimal strategy for the payment of dividends from multiple insurances.\n LOCATION:https://researchseminars.org/talk/RJWAPDE/17/ END:VEVENT END:VCALENDAR