# Quantitative unique continuation of solutions to higher order elliptic equations with singular coefficients

## TL;DR

This paper studies how solutions to complex higher order elliptic equations with singular coefficients behave near points of vanishing, providing new estimates that quantify their unique continuation properties.

## Contribution

It introduces novel quantitative Carleman estimates and characterizes the vanishing order of solutions based on coefficient norms for higher order elliptic equations.

## Key findings

- Established new quantitative Carleman estimates.
- Characterized vanishing order in terms of coefficient Lebesgue norms.
- Enhanced understanding of unique continuation with singular coefficients.

## Abstract

We investigate the quantitative unique continuation of solutions to higher order elliptic equations with singular coefficients. Quantitative unique continuation described by the vanishing order is a quantitative form of strong unique continuation property. We characterize the vanishing order of solutions for higher order elliptic equations in terms of the norms of coefficient functions in their respective Lebesgue spaces. New versions of quantitative Carleman estimates are established.