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.
$σ-$finiteness of a certain Borel measure associated with a positive weak solution to a quasilinear elliptic PDE in space
Hausdorff dimension and $σ$ finiteness of $p-$harmonic measures in space when $p\geq n$
Microlocal approach to the Hausdorff dimension of measures
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