AcademicArticleSCO_84928243350 Academic Article in Scopus uri icon

abstract

  • © 2015 Elsevier Inc.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.

publication date

  • June 15, 2015