Boundary value problems for harmonic functions on a domain in the Sierpinski gasket Justin OwenRobert Strichartz 28A80Sierpinski gasketboundary value problemsPoisson integral formulaDirichlet-to-Neumann mapHaar series expansions 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. Indiana University Mathematics Journal 2012 text pdf 10.1512/iumj.2012.61.4539 10.1512/iumj.2012.61.4539 en Indiana Univ. Math. J. 61 (2012) 319 - 335 state-of-the-art mathematics http://iumj.org/access/