Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Overdetermined Boundary Value Problems, Quadrature Domains and Applications

Overdetermined Boundary Value Problems, Quadrature Domains and Applications We discuss an overdetermined problem in planar multiply connected domains Ω. This problem is solvable in Ω if and only if Ω 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Overdetermined Boundary Value Problems, Quadrature Domains and Applications

Loading next page...
 
/lp/springer-journals/overdetermined-boundary-value-problems-quadrature-domains-and-zzS7ocOXOu
Publisher
Springer Journals
Copyright
Copyright © Heldermann  Verlag 2005
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/bf03321084
Publisher site
See Article on Publisher Site

Abstract

We discuss an overdetermined problem in planar multiply connected domains Ω. This problem is solvable in Ω if and only if Ω 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.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Aug 1, 2005

Keywords: Overdetermined boundary value problem; quadrature domain; analytic function; quadratic differential; 30E25; 30F30; 76D27; 35A30; 35R35

References