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STABILITY AND REGULARITY OF HIGHER ORDER ELLIPTIC OPERATORS WITH MEASURABLE COEFFICIENTS

Published online by Cambridge University Press:  01 October 1998

G. BARBATIS
G. BARBATIS
Affiliation:
6 Irodotou Street, Halandri, 15231 Athens, Greece
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Abstract

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.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 58 , Issue 2 , October 1998 , pp. 342 - 352
Copyright
The London Mathematical Society 1998

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