A Cauchy Integral Formula for Inframonogenic Functions in Clifford Analysis

Boundary value problems for a second‐order elliptic partial differential equation system in Euclidean space

“…A Cauchy-Kowalevski extension theorem for inframonogenic functions appears in [6] and a peculiar connection with the solutions of the Lamé-Navier system in linear elasticity theory is derived in [13,16,17]. More recently in [7][8][9], one defined subclasses of biharmonic functions, which may be understood as somewhat exotic generalization of inframonogenic functions, via the so-called structural sets (to be used mainly in Section 4.2).…”

“…The solutions of this "sandwich" equation were called inframonogenic functions. Given its diverse characteristics, the subject of inframonogenicity has been of increasing interest for mathematicians [7][8][9][10][11][12][13][14][15]. In particular such a functions have been applied to the well-known Lamé-Navier system, which is of considerable interest in practice [16,17].…”

Reduced‐quaternion inframonogenic functions on the ball

“…In earlier studies [1, 2], the term “inframonogenic function” was used for solutions of a two‐sided or “sandwich” second‐order differential equation of the form $$$$ \overline{\partial}f\overline{\partial}=0. $$$$ In the papers cited as well as in more recent work [3–7], the symbol $$$ \overline{\partial} $$$ refers to the Dirac operator $$$ {\sum}_{i=1}^n{\partial}_i{e}_i $$$, where $$$ {\partial}_i $$$ denotes $$$ \partial /\partial {x}_i $$$, while $$$ {e}_i $$$ are the units of the Clifford algebra under consideration. A rather different theory results when one uses for $$$ \overline{\partial} $$$ what is sometimes called the generalized Cauchy–Riemann (or Fueter) operator $$$ {\partial}_0+{\sum}_{i=1}^n{\partial}_i{e}_i $$$, as we propose to carry out here.…”

“…In the papers cited as well as in more recent work [3][4][5][6][7], the symbol 𝜕 refers to the Dirac operator ∑ n i=1 𝜕 i e i , where 𝜕 i denotes 𝜕∕𝜕x i , while e i are the units of the Clifford algebra under consideration. A rather different theory results when one uses for 𝜕 what is sometimes called the generalized Cauchy-Riemann (or Fueter) operator 𝜕 0 + ∑ n i=1 𝜕 i e i , as we propose to carry out here.…”

Looking for structures in the solutions of a generalized lamé-navier system

“…Se arriban a dos posibles generalizaciones en ℝ * : Las funciones dos veces continuamente diferenciables que anulan el operador 𝜕𝜕 3 [⋅]𝜕𝜕 / son llamadas funciones (𝜙𝜙, 𝜓𝜓)-inframonogénicas (Alfonso Santiesteban et al, 2021) y son una extensión de las hoy conocidas funciones inframonogénicas. Estudios de las funciones inframonogénicas se pueden encontrar en Malonek et al (2010), Malonek et al (2011), Moreno García et al (2017), Moreno García et al (2018), y Moreno García et al (2020.…”