Gradient estimates and the fundamental solution for higher-order elliptic systems with lower-order terms

TL;DR

This paper develops gradient estimates and constructs the fundamental solution for higher-order elliptic systems with lower-order terms, extending classical inequalities and analysis techniques to more complex differential equations.

Contribution

It introduces new gradient estimates and constructs fundamental solutions for higher-order elliptic systems with lower-order terms, advancing the theoretical understanding of such equations.

Findings

Established the Caccioppoli inequality for these systems

Proved a reverse H"older inequality similar to Meyers' estimate

Constructed the fundamental solution for linear elliptic equations of order 2m

Abstract

We establish the Caccioppoli inequality, a reverse H\"older inequality in the spirit of the classic estimate of Meyers, and construct the fundamental solution for linear elliptic differential equations of order $2m$ with certain lower order terms.