Quantitative uniqueness for the power of Laplacian with singular coefficients

Details Quantitative uniqueness for the power of Laplacian with singular coefficients Quantitative uniqueness for the power of Laplacian with singular coefficients

2008-03-07

arxiv.org/abs/0803.1012v1

Mathematics

Analysis of PDEs

18 pages

Scientific paper

In this paper we study the local behavior of a solution to the $l$th power of 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.

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