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.

UDC: 517.55

Received: 18.09.2009
Received in revised form: 25.10.2009
Accepted: 10.11.2009

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