Monday Analysis Seminar: Modulus of continuity of p-Dirichlet solutions in a metric measure space

2011-5-9 14:45 - 2011-5-9 16:45
Faculty of Science Buliding #3 Room 210
Tsubasa Itoh (Department of Mathematics, Hokkaido University)
Let $p>1$ and let $X$ be a metric measure space
with a doubling measure and a $(1,p)$-Poincare inequality.
Let $\Omega$ be a bounded p-regular domain in $X$.
It is well known that if a boundary data $f$ is continuous,
then the $p$-Dirichlet solution of $f$ over $\Omega$ is
$p$-harmonic in $\Omega$ and continuous up to the boundary.
We characterize the family of domains such that
improved continuity of boundary functions ensures
improved continuity of the $p$-Dirichlet solution.