Uniqueness of normalized homeomorphic solutions to nonlinear Beltrami equations

Kari Astala; Albert Clop; Daniel Faraco; Jarmo Jääskeläinen; László Székelyhidi

Uniqueness of normalized homeomorphic solutions to nonlinear Beltrami equations

Analysis of PDEs 2010-12-14 v1 Complex Variables

Authors: Kari Astala , Albert Clop , Daniel Faraco , Jarmo Jääskeläinen , László Székelyhidi

Abstract

We settle the problem of the uniqueness of normalized homeomorphic solutions to nonlinear Beltrami equations $\bar\partial f(z)=H(z, \partial f(z))$ . It turns out that the uniqueness holds under definite and explicit bounds on the ellipticity at infinity, but not in general.

Keywords

nonlinear Beltrami equations normalized homeomorphic solutions uniqueness ellipticity at infinity quasiconformal mappings

Cite

@article{arxiv.1012.2827,
  title  = {Uniqueness of normalized homeomorphic solutions to nonlinear Beltrami equations},
  author = {Kari Astala and Albert Clop and Daniel Faraco and Jarmo Jääskeläinen and László Székelyhidi},
  journal= {arXiv preprint arXiv:1012.2827},
  year   = {2010}
}

Comments

12 pages

Related papers

View all related →