Quantitative uniqueness for elliptic equations with singular lower order terms

Abstract

We use a Carleman type inequality of Koch and Tataru to obtain quantitative estimates of unique continuation for solutions of second order elliptic equations with singular lower order terms. First we prove a three sphere inequality and then describe two methods of propagation of smallness from sets of positive measure.

23 pages, v2 small changes are done and some mistakes are corrected

References in corpus (1)

• The stability for the Cauchy problem for elliptic equations

Cited by in corpus (5)

• A stabilized finite element method for inverse problems subject to the convection-diffusion equation. I: diffusion-dominated regime
• Quantitative uniqueness of solutions to second order elliptic equations with singular lower order terms
• New Stability Estimates for the Inverse Medium Problem with Internal Data
• Propagation of smallness for an elliptic PDE with piecewise Lipschitz coefficients
• Quantitative unique continuation and observability on an equidistributed set for the diffusion equation in R^N