Quantitative uniqueness for the power of the Laplacian with singular coefficients
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 10 (2011) no. 3, pp. 513-529.

In this paper we study the local behavior of a solution to the l-th power of the Laplacian with singular coefficients in lower order terms. We obtain a bound on the vanishing order of the nontrivial solution. Our proofs use Carleman estimates with carefully chosen weights. We will derive appropriate three-sphere inequalities and apply them to obtain doubling inequalities and the maximal vanishing order.

Published online:
Classification: 35J15, 35A02
Lin, Ching-Lung 1; Nagayasu, Sei 2; Wang, Jenn-Nan 3

1 Department of Mathematics NCTS, National Cheng Kung University Tainan 701, Taiwan
2 Department of Mathematics Taida Institute for Mathematical Sciences National Taiwan University Taipei 106, Taiwan
3 Department of Mathematics Taida Institute of Mathematical Sciences NCTS (Taipei), National Taiwan University Taipei 106, Taiwan
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Lin, Ching-Lung; Nagayasu, Sei; Wang, Jenn-Nan. Quantitative uniqueness for the power of the Laplacian with singular coefficients. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 10 (2011) no. 3, pp. 513-529. http://archive.numdam.org/item/ASNSP_2011_5_10_3_513_0/

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