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 |