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 J. Sib. Fed. Univ. Math. Phys., 2009, Volume 2, Issue 4, Pages 506–516 (Mi jsfu97)

On the Cauchy Problem for the Dolbeault Complex in the Sobolev spaces

Dmitry P. Fedchenko

Institute of Mathematics, Siberian Federal University, Krasnoyarsk, Russia

Abstract: 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 $(0,q)$, $0<q<n$, with coefficients from the Sobolev space $H^1(D)$ in the domain $D$.

Keywords: Cauchy problem, Cauchy–Riemann operator, Dolbeault complex.

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UDC: 517.55
Received in revised form: 25.10.2009
Accepted: 10.11.2009

Citation: Dmitry P. Fedchenko, “On the Cauchy Problem for the Dolbeault Complex in the Sobolev spaces”, J. Sib. Fed. Univ. Math. Phys., 2:4 (2009), 506–516

Citation in format AMSBIB
\Bibitem{Fed09} \by Dmitry~P.~Fedchenko \paper On the Cauchy Problem for the Dolbeault Complex in the Sobolev spaces \jour J. Sib. Fed. Univ. Math. Phys. \yr 2009 \vol 2 \issue 4 \pages 506--516 \mathnet{http://mi.mathnet.ru/jsfu97} \elib{https://elibrary.ru/item.asp?id=12956413}