PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Yuxi Zheng, Kris Jenssen.

Title:Absolute continuity of elliptic measure
Seminar:Computational and Applied Mathematics Colloquium
Speaker:Jill Pipher, Brown University
Abstract:
In a (sufficiently regular) domain D in n-dimensional Euclidean space, the continuous functions on the boundary of D determine harmonic functions in D with these boundary values. By functional analysis, and the maximum principle for harmonic functions, there exists a probability measure depending on X which is the representing measure for the (harmonic) solution of this boundary value problem. In nice domains, such as the disk or upper half space, this measure is absolutely continuous with respect to the (Lebesgue) surface measure on the boundary. The Poisson kernels, the density of this measure, can sometimes be computed explicitly. When this theory is extended to the setting of more general elliptic second order equations, one of the main questions is: when will the resulting elliptic measure be absolutely continuous with respect to the natural surface measure on the boundary? We'll explain the ideas involved, and give some new criteria for a positive answer.

Room Reservation Information

Room Number:MB106
Date:04 / 24 / 2009
Time:03:35pm - 04:25pm