Strong unique continuation for a residual stress system with Gevrey coefficients

TL;DR

This paper establishes strong unique continuation properties for an elasticity system with residual stress, assuming coefficients are in the Gevrey class, using Carleman estimates for elliptic operators.

Contribution

It proves strong unique continuation for residual stress systems with Gevrey class coefficients, extending previous results by employing Carleman estimates for elliptic operators.

Findings

Proves strong unique continuation under Gevrey regularity.

Uses Carleman estimates for elliptic operators.

Addresses residual stress systems in elasticity.

Abstract

We consider the problem of the strong unique continuation for an elasticity system with general residual stress. Due to the known counterexamples, we assume the coefficients of the elasticity system are in the Gevrey class of appropriate indices. The main tools are Carleman estimates for product of two second order elliptic operators.