Overdetermined Boundary Value Problems, Quadrature Domains and Applications

Dmitry Khavinson, Alexander Solynin, Dimiter Vassilev

Research output: Contribution to journalArticlepeer-review


We discuss an overdetermined problem in planar multiply connected domains $\Om$. This problem is solvable in $\Om$ if and only if $\Om$ 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.
Original languageEnglish
Pages (from-to)19-48
JournalComputational Methods and Function Theory
StatePublished - Jan 2005


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