Regularity of Solutions to a Class of Infinitely Degenerate Second Order Quasilinear Equations

Abstract

This thesis studies regularity of weak solutions to quasilinear infinitely degenerate second order equations. We show that every weak solution to a certain class of degenerate quasilinear equations of divergence form is continuous, thus completing the result on hypoellipticity. We also study properties of subunit metric spaces associated to degenerate second order operators.