Quantitative uniqueness for the power of Laplacian with singular coefficients

Lin, Ching-Lung; Nagayasu, Sei; Wang, Jenn-Nan

Quantitative uniqueness for the power of Laplacian with singular coefficients

Authors

Lin, Ching-Lung

Nagayasu, Sei

Wang, Jenn-Nan

Description

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.
18 pages