New quantitative unique continuation result for elliptic equations

TL;DR

This paper establishes a novel quantitative unique continuation theorem for elliptic equations using a straightforward proof based on Carleman inequalities, also extending results to the Stokes equation.

Contribution

The paper introduces a new, simple proof technique for quantitative unique continuation for elliptic equations, including extensions to the Stokes system.

Findings

Proved a new quantitative unique continuation result for elliptic equations.

Extended the result to the Stokes equation.

Provided a proof based solely on Carleman inequalities.

Abstract

We prove a new quantitative unique continuation result for elliptic equations from Cauchy data. We provide a simple and direct proof based only on a Carleman inequality. Similar result for the Stokes equation is also shown.