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On the dimension of a certain measure in the plane

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.

preprint2013arXivOpen access
Murat Akman
math.CVmath.AP
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Murat Akman

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