TY - JOUR
T1 - Boundary value problems for hyperholomorphic solutions of two dimensional Helmholtz equation in a fractal domain
AU - Abreu Blaya, Ricardo
AU - Bory Reyes, Juan
AU - Rodríguez Dagnino, Ramón M.
N1 - Publisher Copyright:
© 2015 Elsevier Inc.
PY - 2015/6/15
Y1 - 2015/6/15
N2 - 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.
AB - 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.
KW - Boundary value problems
KW - Fractal geometry
KW - Helmholtz equations
KW - Quaternionic analysis
UR - http://www.scopus.com/inward/record.url?scp=84928243350&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2015.03.103
DO - 10.1016/j.amc.2015.03.103
M3 - Artículo
SN - 0096-3003
VL - 261
SP - 183
EP - 191
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
ER -