Geodesic
On the Cauchy Problem for the Dolbeault Complex in the Sobolev spaces
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 4, pp. 506-516.

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Let $D$ be a bounded domain in $\mathbb C^n$ ($n>1$) with a twice smooth boundary $\partial D$. We describe necessary and sufficient Cauchy problem's solvability conditions for the Dolbeault complex in the space of differential forms of bidegree $(0,q)$, $0$, with coefficients from the Sobolev space $H^1(D)$ in the domain $D$.
Keywords: Cauchy problem, Cauchy–Riemann operator
Mots-clés : Dolbeault complex. 
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Dmitry P. Fedchenko. On the Cauchy Problem for the Dolbeault Complex in the Sobolev spaces. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 4, pp. 506-516. http://geodesic.mathdoc.fr/item/JSFU_2009_2_4_a11/

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