On doubling inequalities for elliptic systems

TL;DR

This paper establishes doubling inequalities for solutions of certain elliptic systems, including the iterated Laplacian and the Lame' system, linking these inequalities to the solutions' global properties.

Contribution

It introduces new doubling inequalities for elliptic systems with specific principal parts, expanding the understanding of solution behavior in elasticity and elliptic PDEs.

Findings

Doubling inequalities depend on global solution properties.

Results apply to iterated Laplacian and Lame' systems.

Enhances analysis of elliptic system solutions.

Abstract

We prove doubling inequalities for solutions of elliptic systems with an iterated Laplacian as diagonal principal part and for solutions of the Lame' system of isotropic linearized elasticity. These inequalities depend on global properties of the solutions.