A remark on irregularity of the  <IMG WIDTH="18" HEIGHT="23" ALIGN="BOTTOM" BORDER="0" SRC="/proc/2008-136-07/S0002-9939-08-09206-X/gif-title0/img1.gif" ALT="$ \overline{\partial}$">-Neumann problem on non-smooth domains期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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A remark on irregularity of the $\overline{\partial}$ -Neumann problem on non-smooth domains

Authors:	Sö nmez Sahutoglu

Institution:	Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1043

Abstract:	It is an observation due to J. J. Kohn that for a smooth bounded pseudoconvex domain $\Omega$ in $\mathbb{C}^n$ there exists such that the $\overline{\partial}$ -Neumann operator on $\Omega$ maps $W^s_{(0,1)}(\Omega)$ (the space of -forms with coefficient functions in -Sobolev space of order ) into itself continuously. We show that this conclusion does not hold without the smoothness assumption by constructing a bounded pseudoconvex domain $\Omega$ in $\mathbb{C}^{2}$ , smooth except at one point, whose $\overline{\partial}$ -Neumann operator is not bounded on $W^s_{(0,1)}(\Omega)$ for any .

Keywords:	$\overline {\partial }$-Neumann problem worm domains

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