generalized Green's theorem

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1 total messages Started by Stephen Vavasis Thu, 29 Oct 1992 23:00

Author: Stephen Vavasis
Date: Thu, 29 Oct 1992 23:00

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I'm looking for a generalization of Green's theorem.

Let Omega be a compact simply-connected region of the plane with
suitably smooth boundary curve Gamma.  One version of Green's
theorem states that if u is harmonic on Omega, then

 IntInt grad(u)*grad(u)  =  Int u*(du/dn)

where IntInt is area integration over Omega, and Int is boundary integration
over Gamma, and du/dn is the normal derivative.

I am looking for a weighted version of this identity: given a weight
function w_1 on Omega, find a weight function w_2 on Gamma such that:
 
 IntInt grad(u)*grad(u)*w_1  =  Int u*(du/dn)*w_2

Thanks,
Steve Vavasis (vavasis@cs.cornell.edu))

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