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Geometry and analysis of groups and manifolds

Behavior of Sobolev functions at infinity

speaker: Pekka Koskela (University of Jyvaskyla)

abstract: Let $u$ be a (continuous) function whose first order distributional gradient is $p$-integrable with $p\ge 1$ strictly less than the dimension of the underlying Euclidean space. Then there is a real number $c$ so that $\lim_{t\to \infty}u(tw)=c$ for almost every $w\in S^{n-1},$ the boundary of the unit ball. When $p$ is larger or equal to the dimension, this conclusion may fail even if $u$ is additionally bounded. I will describe our (joint work with Josh Kline and Khanh Nguyen) attemps towards establishing metric versions of these statements.

timetable:
Thu 29 Jun, 10:30 - 11:30, Aula Dini
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