John Lewis: P-harmonic measure revisited

15:30 – 16:30
Title:
Abstract: The term $p$ harmonic measure refers to a measure associated with a positive weak solution to the $ p $ Laplace equation, ($ \nabla \cdot ( | \nabla u |^{p-2} \nabla u ) = 0$, vanishing on a portion of the boundary of a given domain. For example if $ p = 2 $ this measure could be harmonic measure. In this talk I will discuss recent work with coauthors concerning $p$ harmonic measure in simply connected domains $ \subset \rn{2} $ and $ p $ harmonic measure in Reifenberg flat domains
- Wolff snowflakes $ \subset \rn{n}, n \geq 3, $ Our goal is to
eventually obtain endpoint analogues of work on harmonic measure
(the $ p = 2 $ case) due to L. Carleson, P. Jones, N. Makarov, and
T. Wolff. I hope to convince the audience that we are not too far from our goal.