Quantitative uniqueness of solutions to second order elliptic equations with singular potentials in two dimensions

Authors

Blair Davey, City College of New York
Jiuyi Zhu, Louisiana State University

Document Type

Article

Publication Date

6-1-2018

Abstract

In this article, we study the vanishing order of solutions to second order elliptic equations with singular lower order terms in the plane. In particular, we derive lower bounds for solutions on arbitrarily small balls in terms of the Lebesgue norms of the lower order terms for all admissible exponents. Then we show that a scaling argument allows us to pass from these vanishing order estimates to estimates for the rate of decay of solutions at infinity. Our proofs rely on a new L^p- L^q Carleman estimate for the Laplacian in R².

Publication Source (Journal or Book title)

Calculus of Variations and Partial Differential Equations

Recommended Citation

Davey, B., & Zhu, J. (2018). Quantitative uniqueness of solutions to second order elliptic equations with singular potentials in two dimensions. Calculus of Variations and Partial Differential Equations, 57 (3) https://doi.org/10.1007/s00526-018-1345-7