On the dimension of a certain measure in the plane
Analysis of PDEs
2013-01-25 v1 Complex Variables
Abstract
We study the Hausdorff dimension of a measure related to a positive weak solution of a certain partial differential equation in a simply connected domain in the plane. Our work generalizes work of Lewis and coauthors when the measure is harmonic and also for , the well known theorem of Makarov regarding the Hausdorff dimension of harmonic measure relative to a point in a simply connected domain.
Keywords
Cite
@article{arxiv.1301.5860,
title = {On the dimension of a certain measure in the plane},
author = {Murat Akman},
journal= {arXiv preprint arXiv:1301.5860},
year = {2013}
}
Comments
26 pages