Strong unique continuation for 𝑚-th powers of a Laplacian operator with singular coefficients

Lin, Ching-Lung

doi:10.1090/S0002-9939-06-08740-5

Strong unique continuation for $m$-th powers of a Laplacian operator with singular coefficients
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by Ching-Lung Lin PDF

Proc. Amer. Math. Soc. 135 (2007), 569-578 Request permission

Abstract:

In this paper we prove strong unique continuation for $u$ satisfying an inequality of the form $|\triangle ^m u| \leq f(x,u,Du,\cdots ,D^ku)$, where $k$ is up to $[3m/2]$. 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 $|x|^{2\sigma _1}(\log |x|)^{2\sigma _2}\!\exp (\frac {\beta }{2}(\log |x|)^2)$.

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