TY - JOUR
T1 - Electromagnetic Riemann–Hilbert Boundary Value Problem in Fractal Domains of R2
AU - Peña-Pérez, Yudier
AU - Abreu-Blaya, Ricardo
AU - Bory-Reyes, Juan
AU - Schneider, Baruch
N1 - Publisher Copyright:
© 2022, Mathematica Josephina, Inc.
PY - 2022/7
Y1 - 2022/7
N2 - In this paper we present a hyperholomorphic (associated to the Helmholtz equation) approach to the Riemann–Hilbert boundary value problem (RHBVP for short) in domains of R2 with h- summable boundaries. We apply our results to Maxwell’s system and study an electromagnetic RHBVP for the case time-harmonic. The study is based on a reformulation of the time-harmonic Maxwell system in terms of electromagnetic potentials. The main geometric ingredient is the h- summability condition assumed for domains’ boundaries, which are considered fractals.
AB - In this paper we present a hyperholomorphic (associated to the Helmholtz equation) approach to the Riemann–Hilbert boundary value problem (RHBVP for short) in domains of R2 with h- summable boundaries. We apply our results to Maxwell’s system and study an electromagnetic RHBVP for the case time-harmonic. The study is based on a reformulation of the time-harmonic Maxwell system in terms of electromagnetic potentials. The main geometric ingredient is the h- summability condition assumed for domains’ boundaries, which are considered fractals.
KW - Fractal curves
KW - Maxwell system
KW - Riemann–Hilbert boundary value problem
UR - http://www.scopus.com/inward/record.url?scp=85128890786&partnerID=8YFLogxK
U2 - 10.1007/s12220-022-00929-9
DO - 10.1007/s12220-022-00929-9
M3 - Artículo
AN - SCOPUS:85128890786
SN - 1050-6926
VL - 32
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
IS - 7
M1 - 189
ER -