TY - JOUR
T1 - Generalized Laplacian decomposition of vector fields on fractal surfaces
AU - González-Campos, Daniel
AU - Pérez-de la Rosa, Marco Antonio
AU - Bory-Reyes, Juan
N1 - Publisher Copyright:
© 2021 Elsevier Inc.
PY - 2021/7/15
Y1 - 2021/7/15
N2 - We consider the behavior of generalized Laplacian vector fields on a Jordan domain of R3 with fractal boundary. Our approach is based on properties of the Teodorescu transform and suitable extension of the vector fields. Specifically, the present article addresses the decomposition problem of a Hölder continuous vector field on the boundary (also called reconstruction problem) into the sum of two generalized Laplacian vector fields in the domain and in the complement of its closure, respectively. In addition, conditions on a Hölder continuous vector field on the boundary to be the trace of a generalized Laplacian vector field in the domain are also established.
AB - We consider the behavior of generalized Laplacian vector fields on a Jordan domain of R3 with fractal boundary. Our approach is based on properties of the Teodorescu transform and suitable extension of the vector fields. Specifically, the present article addresses the decomposition problem of a Hölder continuous vector field on the boundary (also called reconstruction problem) into the sum of two generalized Laplacian vector fields in the domain and in the complement of its closure, respectively. In addition, conditions on a Hölder continuous vector field on the boundary to be the trace of a generalized Laplacian vector field in the domain are also established.
KW - Fractals
KW - Quaternionic analysis
KW - Vector field theory
UR - http://www.scopus.com/inward/record.url?scp=85100662290&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2021.125038
DO - 10.1016/j.jmaa.2021.125038
M3 - Artículo
AN - SCOPUS:85100662290
SN - 0022-247X
VL - 499
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
M1 - 125038
ER -