On the degenerate Beltrami equation

V. Gutlyanskiǐ, O. Martio, T. Sugawa, M. Vuorinen

Research output: Contribution to journalArticlepeer-review

41 Citations (Scopus)

Abstract

We study the well-known Beltrami equation under the assumption that its measurable complex-valued coefficient μ(z) has the norm ∥μ∥ = 1. Sufficient conditions for the existence of a homeomorphic solution to the Beltrami equation on the Riemann sphere are given in terms of the directional dilatation coefficients of μ. A uniqueness theorem is also proved when the singular set Sing(μ) of μ is contained in a totally disconnected compact set with an additional thinness condition on Sing(μ).

Original languageEnglish
Pages (from-to)875-900
Number of pages26
JournalTransactions of the American Mathematical Society
Volume357
Issue number3
DOIs
Publication statusPublished - 2005 Mar
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'On the degenerate Beltrami equation'. Together they form a unique fingerprint.

Cite this