Dirichlet Type Problem for 2D Quaternionic Time-Harmonic Maxwell System in Fractal Domains

Yudier Peña Pérez; Ricardo Abreu Blaya; BOSCH PÉREZ, PAUL JESÚS; Juan Bory Reyes

doi:10.1155/2020/4735357

Dirichlet Type Problem for 2D Quaternionic Time-Harmonic Maxwell System in Fractal Domains

Journal

Advances in Mathematical Physics

ISSN

1687-9120

1687-9139

Date Issued

2020

Author(s)

Yudier Peña Pérez

Ricardo Abreu Blaya

BOSCH PÉREZ, PAUL JESÚS

Facultad de Ingeniería

Juan Bory Reyes

Type

Resource Types::text::journal::journal article

Scopus ID

2-s2.0-85079433514

WoS ID

WOS:000514592100003

DOI

10.1155/2020/4735357

URL

https://investigadores.udd.cl/handle/123456789/5541

Abstract

We investigate an electromagnetic Dirichlet type problem for the 2D quaternionic time-harmonic Maxwell system over a great generality of fractal closed type curves, which bound Jordan domains in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:msup><mml:mrow><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>. The study deals with a novel approach of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>h</mml:mi></mml:math>-summability condition for the curves, which would be extremely irregular and deserve to be considered fractals. Our technique of proofs is based on the intimate relations between solutions of time-harmonic Maxwell system and those of the Dirac equation through some nonlinear equations, when both cases are reformulated in quaternionic forms.