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

In the framework of Clifford analysis, we study a second‐order elliptic (generally nonstrongly elliptic) system of partial differential equations of the form: ν∂x_fϑ∂x_=0$$ {}^{\nu}\kern-0.1em {\partial}_{\underset{\_}{x}}{f}^{\vartheta}\kern-0.1em {\partial}_{\underset{\_}{x}}=0 $$, where ν∂x_$$ {}^{\nu}\kern-0.1em {\partial}_{\underset{\_}{x}} $$ stands for the Dirac operator with respect to a structural set ν$$ \nu $$. The solutions of this system are known as (ν,ϑ)$$ \left(\nu, \vartheta \right) $$‐inframonogenic functions. Our main purpose is to describe necessary and sufficient conditions for the solvability of a ∂¯$$ \overline{\partial} $$‐problem associated with the sandwich operator ν∂x_(·)ϑ∂x_$$ {}^{\nu}\kern-0.1em {\partial}_{\underset{\_}{x}}{\left(\cdotp \right)}^{\vartheta}\kern-0.1em {\partial}_{\underset{\_}{x}} $$. [ABSTRACT FROM AUTHOR]