Overdeterminded boundary value problems, quadrature domains and applications
From the summary: We discuss an overdetermined problem in planar multiply connected domains \(\Omega\). This problem is solvable in \(\Omega\) if and only if \(\Omega\) is a quadrature domain carrying a solid-contour quadrature identity for analytic functions. At the same time the existence of such quadrature identity is equivalent to the solvability of a special boundary value problem for analytic functions. We give a complete solution of the problem in some special cases and discuss some applications concerning the shape of electrified droplets and small air bubbles in a fluid flow.
scientific article; zbMATH DE number 5011334
scientific article