Quantitative uniqueness of solutions to second-order elliptic equations with singular lower order terms

Document Type

Article

Publication Date

1-1-2019

Abstract

In this article, we study some quantitative unique continuation properties of solutions to second-order elliptic equations with singular lower order terms. First, we quantify the strong unique continuation property by estimating the maximal vanishing order of solutions. That is, when u is a nontrivial solution to ∆u + W . ▽u + Vu = 0 in some open, connected subset of Rn where n ≥ 3 we characterize the vanishing order of solutions in terms of the norms of V and W in their respective Lebesgue spaces. Then, using these maximal order of vanishing estimates, we establish quantitative unique continuation at infinity results for solutions to ∆u + W . ▽u + Vu = 0 in Rn The main tools in our work are new versions of Lp → Lq Carleman estimates for a range of p and q values.

Publication Source (Journal or Book title)

Communications in Partial Differential Equations

First Page

1217

Last Page

1251

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