English

Symmetries in an overdetermined problem for the Green's function

Analysis of PDEs 2009-12-11 v1

Abstract

We consider in the plane the problem of reconstructing a domain from the normal derivative of its Green's function with pole at a fixed point in the domain. By means of the theory of conformal mappings, we obtain existence, uniqueness, (non-spherical) symmetry results, and a formula relating the curvature of the boundary of the domain to the normal derivative of its Green's function.

Keywords

Cite

@article{arxiv.0912.1935,
  title  = {Symmetries in an overdetermined problem for the Green's function},
  author = {Virginia Agostiniani and Rolando Magnanini},
  journal= {arXiv preprint arXiv:0912.1935},
  year   = {2009}
}

Comments

10 pages

R2 v1 2026-06-21T14:22:05.077Z