TY - JOUR
T1 - Decomposition of inframonogenic functions with applications in elasticity theory
AU - Moreno Garcia, Arsenio
AU - Moreno Garcia, Tania
AU - Abreu Blaya, Ricardo
AU - Bory Reyes, Juan
N1 - Publisher Copyright:
© 2019 John Wiley & Sons, Ltd.
PY - 2020/3/15
Y1 - 2020/3/15
N2 - In this paper, we consider functions satisfying the sandwich equation (Formula presented.), where (Formula presented.) stands for the Dirac operator in (Formula presented.). Such functions are referred as inframonogenic and represent an extension of the monogenic functions, ie, null solutions of (Formula presented.). In particular, for odd m, we prove that a C2-function is both inframonogenic and harmonic in (Formula presented.) if and only if it can be represented in Ω as (Formula presented.) where f1 and f2 are, respectively, left and right monogenic functions in Ω, while f3 and f4 are two-sided monogenic functions there. Finally, in deriving some applications of our results, we have made use of the deep connection between the class of inframonogenic vector fields and the universal solutions of the Lamé-Navier system in (Formula presented.).
AB - In this paper, we consider functions satisfying the sandwich equation (Formula presented.), where (Formula presented.) stands for the Dirac operator in (Formula presented.). Such functions are referred as inframonogenic and represent an extension of the monogenic functions, ie, null solutions of (Formula presented.). In particular, for odd m, we prove that a C2-function is both inframonogenic and harmonic in (Formula presented.) if and only if it can be represented in Ω as (Formula presented.) where f1 and f2 are, respectively, left and right monogenic functions in Ω, while f3 and f4 are two-sided monogenic functions there. Finally, in deriving some applications of our results, we have made use of the deep connection between the class of inframonogenic vector fields and the universal solutions of the Lamé-Navier system in (Formula presented.).
KW - Almansi decomposition
KW - Clifford analysis
KW - Lamé system
KW - inframonogenic functions
KW - linear elasticity
UR - http://www.scopus.com/inward/record.url?scp=85074753317&partnerID=8YFLogxK
U2 - 10.1002/mma.6015
DO - 10.1002/mma.6015
M3 - Artículo
SN - 0170-4214
VL - 43
SP - 1915
EP - 1924
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
IS - 4
ER -