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Regularity of the \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\overline{\partial }}$\end{document} ‐equation and Liouville's theorem for pseudoconcave compacts in \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${{\mathbb {C}}{\mathbb {P}}^n}$\end{document}
Author(s) -
Brinkschulte Judith
Publication year - 2013
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201200104
Subject(s) - boundary (topology) , physics , domain (mathematical analysis) , combinatorics , mathematics , mathematical physics , mathematical analysis
We prove regularity results for the \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\overline{\partial }$\end{document} ‐equation for \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {O}(-m)$\end{document} ‐valued forms in the Sobolev spaces W 1 − ε on pseudoconcave domains with \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {C}^2$\end{document} boundary in \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathbb {C}}{\mathbb {P}}^n$\end{document} . We also show that the holomorphic sections of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {O}(-m)$\end{document} of class W 1 − ε vanish on a pseudoconcave domain with \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {C}^2$\end{document} boundary in \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathbb {C}}{\mathbb {P}}^n$\end{document} .