English

On boundary behavior and Dirichlet problem for Beltrami equations

Complex Variables 2012-01-27 v1

Abstract

We show that arbitrary homeomorphic solutions to the Beltrami equations with generalized derivatives satisfy certain moduli inequalities. On this basis, we develope the theory of the boundary behavior of such solutions and prove a series of criteria for the existence of regular, pseudoregular and multi-valued solutions for the Dirichlet problem to the Beltrami equations in arbitrary Jordan domains and in arbitrary finitely connected domains bounded by mutually disjoint Jordan curves, correspondingly.

Keywords

Cite

@article{arxiv.1201.5570,
  title  = {On boundary behavior and Dirichlet problem for Beltrami equations},
  author = {Denis Kovtonyuk and Igor Petkov and Vladimir Ryazanov and Ruslan Salimov},
  journal= {arXiv preprint arXiv:1201.5570},
  year   = {2012}
}

Comments

28 pages, 2 figures

R2 v1 2026-06-21T20:10:11.783Z