Computational Methods and Function Theory 4 (2004), No. 2, 283--298
Copyright Heldermann Verlag 2004
Eric Schippers
eric_schippers@umanitoba.ca , Department of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada.
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.
Keywords: Green's function, Hadamard variation, Bergman kernel.
MSC 2000: 30C40, 30C70.
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