For more information about this meeting, contact John Roe, Dmitri Burago.
| Title: | How the Monge--Ampere equation helps in proving the John--Nirenberg inequality |
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| Seminar: | Geometry Luncheon Seminar |
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| Speaker: | Vasily Vasyunin, Steklov Institute, St. Petersburg |
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| Abstract: |
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| 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 |
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| Date: | 03 / 23 / 2011 |
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| Time: | 12:20pm - 01:30pm |
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