On the dimension of a certain measure in the plane

@article{Akman2013OnTD,
  title={On the dimension of a certain measure in the plane},
  author={Murat Akman},
  journal={arXiv: Analysis of PDEs},
  year={2013}
}
  • M. Akman
  • Published 24 January 2013
  • Mathematics
  • arXiv: Analysis of PDEs
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 $p$ harmonic and also for $p=2$, the well known theorem of Makarov regarding the Hausdorff dimension of harmonic measure relative to a point in a simply connected domain. 
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