Plemelj formula of inframonogenic functions and their boundary value problems

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

“…){\partial}_{\underset{\_}{x}} $$ keeps the space of $$$ k $$$‐vector fields invariant, and it is verified that $$$$ {\partial}_{\underset{\_}{x}}{F}_k{\partial}_{\underset{\_}{x}}={\left(-1\right)}^k\left({\partial}_{\underset{\_}{x}}\cdotp {\partial}_{\underset{\_}{x}}\wedge {F}_k-{\partial}_{\underset{\_}{x}}\wedge {\partial}_{\underset{\_}{x}}\cdotp {F}_k\right). $$$$ For a recent summary and overview on the inframonogenic function theory, we refer the reader to [7, 8, 11, 14, 15].…”

“…For a recent summary and overview on the inframonogenic function theory, we refer the reader to [7,8,11,14,15]. , called the Moisil-Théodoresco operator; see [18].…”

“…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].…”

∂¯‐problem for a second‐order elliptic system in Clifford analysis

“…The subject of inframonogenicity has been of increasing interest for physicists and mathematicians [2,[4][5][6][7][8][9][10][11][12].…”

“…In the vector calculus context when we restrict ourselves to consider vector‐valued solutions $$$ f=\overrightarrow{u} $$$ in $$$ {\mathrm{\mathbb{R}}}^3 $$$, the above sandwich Equation () can be written in the form $$$$ \operatorname{grad}\kern3pt \operatorname{div}\kern3pt \overrightarrow{u}+{\mathrm{rot}}^2\overrightarrow{u}=0. $$$$ The subject of inframonogenicity has been of increasing interest for physicists and mathematicians [2, 4–12].…”