Sur l'op\'erateur $\bar{\partial}$ et les fonctions diff\'erentiables au sens de Whitney dans un domaine $q$-convexe de $\mathbb{C}^n$

TL;DR

This paper addresses the solution of the arar problem for differential forms within Whitney's framework, specifically in the context of q-convex domains in complex n-space.

Contribution

It provides a solution to the arar problem for Whitney differentiable functions in q-convex domains, extending previous results to this setting.

Findings

Solved the arar problem for Whitney differentiable forms

Extended arar theory to q-convex domains

Established existence results in complex analysis for Whitney functions

Abstract

We solve the $\bar{\partial}$-problem for differential forms in the sens of Whitney.