An $\mathrm{L}^2$-maximum principle for circular arcs on the disk
An $\mathrm{L}^2$-maximum principle for circular arcs on the disk
It is well-known that bounded harmonic functions attain a point-wise maximum on the boundary of the domain. For harmonic functions with general $\mathrm{L}^p, ~p \in [1, \infty)$ boundary data, however, such an $\mathrm{L}^{\infty}$-maximum principle does not hold. In this article, we prove a novel $\mathrm{L}^2$-maximum principle for harmonic functions on …