paper

Quantitative uniqueness for the power of Laplacian with singular coefficients

arXiv:0803.1012

Abstract

In this paper we study the local behavior of a solution to the 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

Quantitative uniqueness for the power of Laplacian with singular coefficients · wovepaper