Quantitative uniqueness for the power of Laplacian with singular coefficients

Abstract

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.

An inverse problem on determining second order symmetric tensor for perturbed biharmonic operator

“…For more on the elasticity model and perturbed biharmonic operators see [10,29,32]. A related study of unique continuation for Kirchoff-Love plate equation or in general fourth-order elliptic equation has its own appeal, we refer [12,13,27,33] and reference therein. Let us also mention the recent work of [2] which studies the boundary unique continuation results for the Kirchoff-Love plate equation.…”

An Inverse Problem on Determining Second Order Symmetric Tensor for Perturbed Biharmonic Operator

“…For more on the elasticity model and perturbed biharmonic operators see [32,30,10]. A related study of unique continuation for Kirchoff-Love plate equation or in general fourth-order elliptic equation has its own appeal, we refer [12,13,28,33] and reference therein. Let us also mention the recent work of [2] which studies the boundary unique continuation results for the Kirchoff-Love plate equation.…”

Global stability for an inverse problem in soil–structure interaction

“…The proof of the above proposition is based on the three spheres inequality obtained by Lin et al [14].…”