English

Cauchy-Pompeiu type formulas for d-bar on affine algebraic Riemann surfaces and some applications

Complex Variables 2010-01-11 v2 Analysis of PDEs

Abstract

We have obtained the explicit versions and precisions for the Hodge-Riemann decomposition of formes on affine algebraic curve V. The main application consists in the construction of Faddeev-Green function for Laplacian on V. Basing on this [HM](arXiv:0804.3951 and J.Geom.Anal., 2008,18), we extended from the case X in C to the case of bordered Riemann surface X in V the R.Novikov (1988) scheme for the effective reconstruction of conductivity function sigma on X through Dirichlet-to-Neumann mapping on bX for solutions of d(sigma d^cU)=0. In Sec.4 we give a correction of the paper [HM].

Keywords

Cite

@article{arxiv.0804.3761,
  title  = {Cauchy-Pompeiu type formulas for d-bar on affine algebraic Riemann surfaces and some applications},
  author = {Gennadi Henkin},
  journal= {arXiv preprint arXiv:0804.3761},
  year   = {2010}
}