A jump problem for β-analytic functions in domains with fractal boundaries

Ricardo Abreu-Blaya, Juan Bory-Reyes, Jean Marie Vilaire

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

Let γ be a simple closed Jordan curve in the complex plane ℂ, ω+ and ω- the corresponding domains in ℂ, with 0 ε ω+ and ∞ ε ω-. The classes of complex valued functions satisfying some boundary conditions as well as integral representations for them are considered. Main goal of this paper is the study of the standard jump Riemann boundary value problem over a fractal curve γ (ℓ+{t) - ℓ- (t) = f(t), t ε γ, where ℓ ±(t) are the boundary values of the β-analytic function ℓ at the point t, approaching the boundary from ω+ and ω,- respectively.

Original languageEnglish
Pages (from-to)105-111
Number of pages7
JournalRevista Matematica Complutense
Volume23
Issue number1
DOIs
StatePublished - Jan 2010
Externally publishedYes

Keywords

  • -analytic functions
  • Fractals
  • Jump problem
  • β

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