Approximation of harmonic functions on metric measure spaces of controlled geometry via discrete graphs

Almaz Butaev, Liangbing Luo, Nageswari Shanmugalingam

Given a complete doubling metric measure space $X$ that supports a $2$-Poincaré inequality, we approximate harmonic functions on a bounded domain $\hat{I}\text{c◯}$ with a prescribed Newton-Sob…