Boundary value problems for hyperholomorphic solutions of two dimensional Helmholtz equation in a fractal domain

Ricardo Abreu Blaya, Juan Bory Reyes and Ramón M. Rodríguez Dagnino

Applied Mathematics and Computation, 2015, vol. 261, issue C, 183-191

Abstract: A theory of quaternion-valued functions, called hyperholomorphic, of two real variables has long been established. This theory is in the same relation to the two dimensional Helmholtz equation as the usual one-dimensional complex analysis is to the Laplace equation in R2. In this work we define a new Cauchy integral for domains with fractal boundary illustrating its applications and usage to study the jump and Dirichlet type boundary value problems in a fractal domain.

Keywords: Quaternionic analysis; Helmholtz equations; Boundary value problems; Fractal geometry (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:261:y:2015:i:c:p:183-191

DOI: 10.1016/j.amc.2015.03.103

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