generalized Green's theorem

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From: 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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From: vavasis@cs.cornell.EDU (Stephen Vavasis)
Newsgroups: sci.math.research
Subject: generalized Green's theorem
Message-ID: <1992Oct29.230057.14842@cs.cornell.edu>
Date: 29 Oct 92 23:00:57 GMT
Article-I.D.: cs.1992Oct29.230057.14842
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Organization: Cornell Univ. CS Dept, Ithaca NY 14853
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