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.
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Schippers, E. Behaviour of Kernel Functions under Homotopic Variations of Planar Domains. Comput. Methods Funct. Theory 4, 283–298 (2005). https://doi.org/10.1007/BF03321070
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DOI: https://doi.org/10.1007/BF03321070