Strong unique continuation for <IMG BORDER="0" SRC="/proc/2007-135-02/S0002-9939-06-08740-5/gif-title0/img1.gif" >-th powers of a Laplacian operator with singular coefficients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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Strong unique continuation for -th powers of a Laplacian operator with singular coefficients

Authors:	Ching-Lung Lin

Institution:	Department of Mathematics, National Chung-Cheng University, Chia-Yi 62117, Taiwan

Abstract:	In this paper we prove strong unique continuation for satisfying an inequality of the form $\vert\triangle^m u\vert \leq f(x,u,Du,\cdots,D^ku)$ , where is up to . This result gives an improvement of a work by Colombini and Grammatico (1999) in some sense. The proof of the main theorem is based on Carleman estimates with three-parameter weights $\vert x\vert^{2\sigma_1}(\log\vert x\vert)^{2\sigma_2}\exp (\frac{\beta}{2}(\log \vert x\vert)^2)$ .

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