PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact John Roe, Dmitri Burago.

Title:How the Monge--Ampere equation helps in proving the John--Nirenberg inequality
Seminar:Geometry Luncheon Seminar
Speaker:Vasily Vasyunin, Steklov Institute, St. Petersburg
Abstract:
I would like to present, using the famous John--Nirenberg inequality as an example, a rather new technique of obtaining integral estimates in analysis, the so-called Bellman function method. Originated in the stochastic control theory, it has become a hands-on and effective tool in proving various functional inequalities. The estimate being proved is recast as the solution of an extremal problem. Solving such problems exactly -- a step that often depends on solving Monge--Amp\`ere equations on problem-specific Euclidean domains -- produces inequalities with sharp constants. The presentation will not require any special knowledge; in particular, one does not need to know what the John--Nirenberg inequality is. The main prerequisite is the Lebesgue integration theory.

Room Reservation Information

Room Number:MB114
Date:03 / 23 / 2011
Time:12:20pm - 01:30pm