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

Abstract

We establish the Caccioppoli inequality, a reverse Hölder inequality in the spirit of the classic estimate of Meyers, and construct the fundamental solution for linear elliptic differential equations of order 2m2m with certain lower order terms.

Keywords

• fundamental solution
• caccioppoli inequality
• reverse hölder inequality
• elliptic partial differential equation
• higher order partial differential equation
• primary 35j08
• secondary 35a23
• 35c15
• 35j48