manuscripta mathematica

, Volume 151, Issue 3–4, pp 375–418 | Cite as

Gradient estimates and the fundamental solution for higher-order elliptic systems with rough coefficients

  • Ariel BartonEmail author


This paper considers the theory of higher-order divergence-form elliptic differential equations. In particular, we provide new generalizations of several well-known tools from the theory of second-order equations. These tools are the Caccioppoli inequality, Meyers’s reverse Hölder inequality for gradients, and the fundamental solution. Our construction of the fundamental solution may also be of interest in the theory of second-order operators, as we impose no regularity assumptions on our elliptic operator beyond ellipticity and boundedness of coefficients.

Mathematics Subject Classification

35J48 31B10 35C15 


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© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Mathematical Sciences309 SCEN, University of ArkansasFayettevilleUSA

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