<div dir="ltr"> SPECIAL SEMINAR <br><br><div><div><div><span class=""><span>Speaker : Murat AKMAN </span></span>(Consejo Superior de Investigaciones Científicas, Madrid)</div><div><span class=""><span>Date : 06.04.2015, at 11:00<br></span></span></div><div><span class=""><span>Place: MSGSÜ Department of Mathematics, Bomonti, Istanbul<br><br></span></span></div><div><span class=""><span><br></span></span></div><div><span class=""><span><br>ON THE SIZE OF SUPPORT OF p-HARMONIC MEASURE IN SPACE<br><br></span></span><span class=""><span>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. </span></span><br><br><span class=""><span>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 $\neq
2$. </span></span><br></div></div></div></div>