On a homotopy formula for generalized steady Stokes' operators, associated with the de Rham complex

Abstract

We construct left, right and bilateral fundamental solutions for generalized steady Stokes' operators $S$ with smooth coefficients coefficients, associated with the de Rham complex of differentials on differential forms over a domain $X$ in ${\mathbb R}^n$. The investigated operators are Douglis-Nirenberg elliptic under reasonable assumptions. As an immediate corollary we produce a homotopy formula for regular solutions to this operator.