[Turkmath:376] MSGSÜ Special Seminar, Murat Akman, 06.04.2015, 11:00

[Kıvanç Ersoy]

                 SPECIAL SEMINAR

Speaker  : Murat AKMAN   (Consejo Superior de Investigaciones Científicas,
Madrid)
Date : 06.04.2015, at 11:00
Place: MSGSÜ Department of Mathematics, Bomonti, Istanbul



ON THE SIZE OF SUPPORT OF p-HARMONIC MEASURE IN SPACE

A function $u$ is said to be p-harmonic, fixed $1<p<\infty$, in an open set
$\Omega\subset\mathbb{R}^{n}$ if $u$ is a weak solution to the p-Laplace
equation $\nabla \cdot (|\nabla u|^{p-2} \nabla u)=0$ in $\Omega$. This pde
is nonlinear elliptic equation in divergence form and when $p=2$, it is the
Laplace equation which is linear elliptic equation.

In this talk we study the size of the support of p-harmonic measure
associated with a positive p-harmonic function in
$\Omega\subset\mathbb{R}^{n}$ with certain boundary values. We first
discuss a recent work on ``natural generalization'' of a well-known result
of Jones and Wolff for harmonic measure to the p-harmonic setting when
$p\geq n$. We then study singular sets for p-harmonic measure on ``flat''
domains. Finally, we propose some questions which is known in the harmonic
setting but not known in the p-harmonic setting for $\neq 2$.
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