Mean-Value Inequalities for Harmonic Functions
Stefan Steinerberger (University of Washington)
Abstract: The mean-value theorem for harmonic functions says that we can bound the integral of a harmonic function in a ball by the average value on the boundary (and, in fact, there is equality). What happens if we replace the ball by a general convex or even non-convex set? As it turns out, this simple question has connections to classical potential theory, probability theory, PDEs and even mechanics: one of the arising questions dates back to Saint Venant (1856). There are some fascinating new isoperimetric problems: for example, the worst case convex domain in the plane seems to look a lot like the letter "D" but we cannot prove it. I will discuss some recent results and many open problems.
analysis of PDEsclassical analysis and ODEsfunctional analysismetric geometry
Audience: researchers in the topic
Series comments: Description: A senior graduate student/postdoc series in harmonic analysis, geometric measure theory, and partial differential equations.
Meetings will be weekly, and usually will occur on Monday, with some exceptions. For each talk, the Zoom link is made available in the website too. Contact Bruno Poggi at poggi008@umn.edu if you would like to subscribe to the seminar mailing list.
| Organizers: | Bruno Poggi*, Ryan Matzke, Jose Luis Luna Garcia* |
| *contact for this listing |