STABILITY AND REGULARITY OF HIGHER ORDER ELLIPTIC OPERATORS WITH MEASURABLE COEFFICIENTS.

In this paper, we investigate two problems concerning a class of higher order uniformly elliptic operators with measurable coefficients. In our first result, we prove a stability estimate for the resolvent of such an operator under perturbation of its principal coefficients in Lp spaces. Our second result is a regularity theorem concerning the smoothing properties of the resolvent, and it provides a sufficient condition under which the first result can be applied. [ABSTRACT FROM AUTHOR]