Generalized Laplacian decomposition of vector fields on fractal surfaces
Complex Variables
2021-02-11 v3
Abstract
We consider the behavior of generalized Laplacian vector fields on a Jordan domain of 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 H\"older 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 H\"older continuous vector field on the boundary to be the trace of a generalized Laplacian vector field in the domain are also established.
Keywords
Cite
@article{arxiv.2002.01899,
title = {Generalized Laplacian decomposition of vector fields on fractal surfaces},
author = {Daniel González Campos and Marco Antonio Pérez de la Rosa and Juan Bory Reyes},
journal= {arXiv preprint arXiv:2002.01899},
year = {2021}
}