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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     author = {Dmitry P. Fedchenko},
     title = {On the {Cauchy} {Problem} for the {Dolbeault} {Complex} in the {Sobolev} spaces},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {506--516},
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     volume = {2},
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     year = {2009},
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     url = {http://geodesic.mathdoc.fr/item/JSFU_2009_2_4_a11/}
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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/