Analysis Seminar - Up to the Boundary Gradient Estimates in Bernoulli Type Free Boundary Problems

Explore recent advancements in up-to-the-boundary gradient estimates for viscosity solutions of free boundary problems in this analysis seminar presented by Diego Moreira from Universidade Federal do Ceará, Fortaleza, Brazil. Delve into the study of fully nonlinear and quasilinear equations with unbounded coefficients, and discover the innovative use of Inhomogeneous Pucci Barriers as new proof elements. Examine key steps in the proof process, including the trace estimate of the solution on fixed boundary points that project non-tangentially over the free boundary. Gain insights into methods inspired by Carlos Kenig's ideas in Harmonic Analysis, and enhance your understanding of Bernoulli-type free boundary problems in mathematical analysis.