Mathematical Physics and Harmonic Analysis Seminar

Date: November 20, 2020

Time: 1:50PM - 2:50PM

Location: Zoom

Speaker: Eduardo Teixeira, University of Central Florida

Title: Shaping diffusion in non-variational models

Abstract: Mathematical models yielding diffusion adjustments are relevant in several fields of research and by now a comprehensive variational theory for treating such problems is well established. The corresponding non-variational theory has been completely open, despite of its potential applicabilities and in this talk I will describe some recent efforts towards launching such a theory. We will introduce a new class of non-divergence form elliptic operators whose degree of degeneracy/singularity varies accordantly to a prescribed power law. Under rather general conditions, we prove viscosity solutions are differentiable, with appropriate (universal) estimates. This result opens a number of new lines of investigation and I'll describe some of these endeavors towards the end of the talk.