# MathSciDoc: An Archive for Mathematician ∫

#### TBDmathscidoc:1701.333033

Arkiv for Matematik, 42, (2), 259-282, 2002.12
We consider a domain Ω with Lipschitz boundary, which is relatively compact in an$n$-dimensional Kähler manifold and satisfies some “logδ-pseudoconvexity” condition. We show that the $$\bar \partial$$ -equation with exact support in ω admits a solution in bidegrees ($p, q$), 1≤$q$≤$n$−1. Moreover, the range of $$\bar \partial$$ acting on smooth ($p, n$−1)-forms with support in $$\bar \Omega$$ is closed. Applications are given to the solvability of the tangential Cauchy-Riemann equations for smooth forms and currents for all intermediate bidegrees on boundaries of weakly pseudoconvex domains in Stein manifolds and to the solvability of the tangential Cauchy-Riemann equations for currents on Levi flat$CR$manifolds of arbitrary codimension.
@inproceedings{judith2002the,
title={The $$\bar \partial$$ -problem with support conditions on some weakly pseudoconvex domainswith support conditions on some weakly pseudoconvex domains},
author={Judith Brinkschulte},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203611212858842},
booktitle={Arkiv for Matematik},
volume={42},
number={2},
pages={259-282},
year={2002},
}

Judith Brinkschulte. The $$\bar \partial$$ -problem with support conditions on some weakly pseudoconvex domainswith support conditions on some weakly pseudoconvex domains. 2002. Vol. 42. In Arkiv for Matematik. pp.259-282. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203611212858842.