Gradient Estimates and the Fundamental Solution for Higher-Order Elliptic Systems with Lower-Order Terms

Authors

Ariel E. Barton, University of Arkansas, FayettevilleFollow
Michael J. Duffy Jr., University of Arkansas, FayettevilleFollow

Document Type

Article

Publication Date

5-2023

Keywords

fundamental solution; Caccioppoli inequality; reverse Holder inequality; elliptic partial differential equation; higher order partial differential equation

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 2m with certain lower order terms.

Citation

Barton, A. E., & Duffy, M. J. (2023). Gradient Estimates and the Fundamental Solution for Higher-Order Elliptic Systems with Lower-Order Terms. Advanced Nonlinear Studies, 23 (1), 20220064. https://doi.org/10.1515/ans-2022-0064

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.