# Unique continuation property with partial information for two-dimensional anisotropic elasticity systems

## TL;DR

This paper proves a new unique continuation property for 2D anisotropic elasticity systems, showing that partial information about one component can determine the entire solution, reducing data requirements significantly.

## Contribution

It introduces a novel unique continuation result using Riemann functions, allowing determination of solutions with minimal partial data in anisotropic elasticity systems.

## Key findings

- Solution vanishes in the whole domain if one component vanishes in a subdomain and the other component's derivatives vanish at a point.
- Constructs examples demonstrating further reduction of data needed for unique continuation.
- Data requirement for unique determination is nearly halved, enhancing practical applicability.

## Abstract

In this paper, we establish a novel unique continuation property for two-dimensional anisotropic elasticity systems with partial information. More precisely, given a homogeneous elasticity system in a domain, we investigate the unique continuation by assuming only the vanishing of one component of the solution in a subdomain. Using the corresponding Riemann function, we prove that the solution vanishes in the whole domain provided that the other component vanishes at one point up to its second derivatives. Further, we construct several examples showing the possibility of further reducing the additional information of the other component. This result possesses remarkable significance in both theoretical and practical aspects because the required data is almost halved for the unique determination of the whole solution.