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We solve the $\partial \bar{\partial}$-problem for a form with distributionboundary value on a strongly pseudoconvex contractible domain of a complexmanifold.

R{\'e}solution du $\partial \bar{\partial}$ pour les formes  diff{\'e}rentielles ayant une valeur au bord au sens des courants  d{\'e}finies dans un domaine contractile fortement pseudoconvexe d'une  vari{\'e}t{\'e} complexe