Mathematics

Starting with results by Moser, Nash, and DeGiorgi in the late 50's-early 60's, the regularity theory of elliptic and subelliptic equations with rough coefficients has been thoroughly developed. There is also a smaller theory still in its infancy of infinitely degenerate elliptic equations with smooth data, beginning with work of Fedii and Kusuoka-Strook, and continued by Morimoto and Christ. In this talk I will present our results that initiate a regularity theory in the context of equations that are both infinitely degenerate elliptic and have rough data. More precisely, I will talk about local boundedness and continuity of weak solutions via DeGiorgi iterations, for a certain class of infinitely degenerate elliptic equations with rough coefficients.