Up to the boundary gradient estimates for solutions to nonlinear free boundary problems with unbounded measurable ingredients

Abstract: In this talk, we discuss recent advances on up to the boundary gradient estimates for viscosity solutions of free boundary problems governed by fully nonlinear and quasilinear equations with unbounded coefficients. We present the new Inhomogeneous Pucci Barriers as new elements for the proof. If time permits, we discuss some of the main steps in the proof, namely, the trace estimate of the solution on the points of the fixed boundary that projects nontangentially over the free boundary. These methods are inspired by some ideas of Carlos Kenig in Harmonic Analysis.

analysis of PDEs

Audience: researchers in the topic

Rio de Janeiro webinar on analysis and partial differential equations

Series comments: Talks are held twice a month; start time and day of the week may vary, according to the speaker time zone. A link to join each webinar will be made available in due time here and at sites.google.com/view/webinarpde/home