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

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Abstract

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.

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  1. Department of Mathematical Sciences, 309 SCEN, University of Arkansas, Fayetteville, AR, 72701, USA

    Ariel Barton

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Barton, A. Gradient estimates and the fundamental solution for higher-order elliptic systems with rough coefficients. manuscripta math. 151, 375–418 (2016). https://doi.org/10.1007/s00229-016-0839-x

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