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The $$\bar \partial $$ -problem with support conditions on some weakly pseudoconvex domainswith support conditions on some weakly pseudoconvex domains

Judith Brinkschulte Mathematisches Institut, Universität Leipzig

TBD mathscidoc: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.
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@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.
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