IUMJ

Title: Boundary value problems for harmonic functions on a domain in the Sierpinski gasket

Authors: Justin Owen and Robert S. Strichartz

Issue: Volume 61 (2012), Issue 1, 319-335

Abstract:

For a certain domain $D$ in the Sierpinski Gasket (SG) whose boundary is a line segment $L$, we give an explicit analogue of the Poisson integral formula to recover a harmonic function $u$ on $D$ from its boundary values $f$ on $L$ in terms of the Haar series expansion of $f$, and we characterize these as belonging to natural function spaces on $D$ by $f$ belonging to appropriate function spaces on $L$. We also give a Dirichlet-to-Neumann map on $L$ as a Haar series multiplier transformation.