Jose Luis Luna Garcia

University of Missouri, Columbia

Talk Title: Solvability of Elliptic Equations with Lower Order Terms

Abstract: The study of boundary value problems for purely second order elliptic equations in the upper half space or a Lipschitz domain has a long and celebrated history. In this talk we will focus on generalizing well-posedness of the standard Boundary Value Problems (i.e. Dirichlet, Neumann and Regularity), in the upper half space, to equations with lower order terms (drift terms and a potential). Our results state roughly that, if the lower order terms are sufficiently small in a critical Lebesgue space norm, then the well-posedness (appropriately defined) of these Boundary Value Problems is inherited from the corresponding property for the purely second order equation.