DECAY OF A p-HARMONIC MEASURE IN THE PLANE
Artikel i vetenskaplig tidskrift, 2013

We study the asymptotic behaviour of a p-harmonic measure w(p), p is an element of (1, infinity], in a domain Omega subset of R-2, subject to certain regularity constraints. Our main result is that w(p) (B (w, delta) boolean AND partial derivative Omega, w(0)) approximate to delta(q) as delta -> 0(+), where q = q(v,p) is given explicitly as a function of v and p. Here, v is related to properties of Omega near w. If p = infinity, this extends to some domains in R-n. By a result due to Hirata, our result implies that the p-Green function for p is an element of (1, 2) is not quasi-symmetric in plane C-1,C-1-domains.

harmonic function

p-Laplace operator

Harmonic measure

generalized interior ball

Författare

N. L. P. Lundstrom

Umea universitet

Jonatan Vasilis

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Annales Academiae Scientiarum Fennicae Mathematica

1239-629X (ISSN)

Vol. 38 351-366

Ämneskategorier

Matematik

DOI

10.5186/aasfm.2013.3808