Decay of a p-harmonic measure in the plane
2013 (English)In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 38, no 1, 351-366 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
Suomalainen Tiedeakatemia , 2013. Vol. 38, no 1, 351-366 p.
harmonic measure, harmonic function, p-Laplace operator, generalized interior ball
Mathematics Mathematical Analysis
Research subject Mathematics; Mathematical Statistics
IdentifiersURN: urn:nbn:se:umu:diva-47922DOI: 10.5186/aasfm.2013.3808ISI: 000316239200019OAI: oai:DiVA.org:umu-47922DiVA: diva2:445350
Originally published in thesis in manuscript form2011-10-032011-10-032014-09-15Bibliographically approved