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Behaviour of Kernel Functions under Homotopic Variations of Planar Domains

Behaviour of Kernel Functions under Homotopic Variations of Planar Domains A variational formula is derived for Green’s function of multiply connected planar domains under homotopy of the boundary. The formula shows that up to first order, a homotopy behaves like the Hadamard variation. This is applied to show that certain expressions in the derivatives of Green’s function are monotonic with respect to set inclusion. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Behaviour of Kernel Functions under Homotopic Variations of Planar Domains

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References (11)

Publisher
Springer Journals
Copyright
Copyright © Heldermann  Verlag 2004
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/bf03321070
Publisher site
See Article on Publisher Site

Abstract

A variational formula is derived for Green’s function of multiply connected planar domains under homotopy of the boundary. The formula shows that up to first order, a homotopy behaves like the Hadamard variation. This is applied to show that certain expressions in the derivatives of Green’s function are monotonic with respect to set inclusion.

Journal

Computational Methods and Function TheorySpringer Journals

Published: May 1, 2005

Keywords: Hadamard variation; Bergman kernel; 30C40; 30C70

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