Strong unique continuation for two-dimensional anisotropic elliptic systems

TL;DR

This paper establishes the strong unique continuation property for 2D anisotropic elliptic systems with real coefficients, using Carleman estimates and system transformation techniques.

Contribution

It introduces a novel approach to prove strong unique continuation for anisotropic elliptic systems in Gevrey class by transforming the system and deriving new Carleman estimates.

Findings

Proves strong unique continuation for 2D anisotropic elliptic systems.

Develops Carleman estimates based on system transformation.

Handles systems with simple characteristic principal symbols.

Abstract

In this paper, we give the strong unique continuation property for a general two dimensional anisotropic elliptic system with real coefficients in a Gevrey class under the assumption that the principal symbol of the system has simple characteristics. The strong unique continuation property is derived by obtaining some Carleman estimate. The derivation of the Carleman estimate is based on transforming the system to a larger second order elliptic system with diagonal principal part which has complex coefficients.