Monday Analysis Seminar: Modulus of continuity of pDirichlet solutions in a metric measure space
 Date

201159 14:45 
201159 16:45
 Place
 Faculty of Science Buliding #3 Room 210

Speaker/Organizer
 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 pregular 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.