Boundary multifractal behaviour for harmonic functions in the ball

Details Boundary multifractal behaviour for harmonic functions in the ball Boundary multifractal behaviour for harmonic functions in the ball

2011-10-26

arxiv.org/abs/1110.5780v2

Mathematics

Classical Analysis and ODEs

16 pages

Scientific paper

It is well known that if $h$ is a nonnegative harmonic function in the ball of $\RR^{d+1}$ or if $h$ is harmonic in the ball with integrable boundary values, then the radial limit of $h$ exists at almost every point of the boundary. In this paper, we are interested in the exceptional set of points of divergence and in the speed of divergence at these points. In particular, we prove that for generic harmonic functions and for any $\beta\in [0,d]$, the Hausdorff dimension of the set of points $\xi$ on the sphere such that $h(r\xi)$ looks like $(1-r)^{-\beta}$ is equal to $d-\beta$.

Affiliated with

Also associated with

No associations

Rating

Boundary multifractal behaviour for harmonic functions in the ball does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Boundary multifractal behaviour for harmonic functions in the ball, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Boundary multifractal behaviour for harmonic functions in the ball will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-717085