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

Author

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

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.

Suggested Citation

  • Abreu Blaya, Ricardo & Bory Reyes, Juan & Rodríguez Dagnino, Ramón M., 2015. "Boundary value problems for hyperholomorphic solutions of two dimensional Helmholtz equation in a fractal domain," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 183-191.
    • Handle: RePEc:eee:apmaco:v:261:y:2015:i:c:p:183-191
    DOI: 10.1016/j.amc.2015.03.103
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