A New Generation of Calderon-Zygmund Theory with Applications to Boundary Value Problems

Thursday, April 28, 2016 - 4:00pm
110 MSB
Brock Schmutzler (Advisor: Prof. Marius Mitrea)

Abstract: I will be presenting a theory of singular integral operators, of Calderon-Zygmund type, capable of handling the boundary layer potentials arising naturally in the treatment of elliptic boundary value problems in rough subdomains of Riemannian manifolds.  This includes nontangential boundedness and pointwise traces (jump formulas), square-function and Carleson measure estimates, as well as compactness criteria on Lebesgue and Sobolev spaces.  The nature of the underlying domain is very general, and is best described in the language of geometric measure theory.