  We extend several well-known tools from the theory of second-order
divergence-form elliptic equations to the case of higher-order equations. These
tools are the Caccioppoli inequality, Meyers's reverse Holder 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.
