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Abstract and Applied Analysis
Volume 2014, Article ID 274859, 8 pages
http://dx.doi.org/10.1155/2014/274859
Research Article

High Order Fefferman-Phong Type Inequalities in Carnot Groups and Regularity for Degenerate Elliptic Operators plus a Potential

Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi 710129, China

Received 4 June 2014; Accepted 13 October 2014; Published 10 November 2014

Academic Editor: Sung G. Kim

Copyright © 2014 Pengcheng Niu and Kelei Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be the basis of space of horizontal vector fields in a Carnot group . We prove high order Fefferman-Phong type inequalities in . As applications, we derive a priori estimates for the nondivergence degenerate elliptic operators with coefficients and a potential belonging to an appropriate Stummel type class introduced in this paper. Some of our results are also new even for the usual Euclidean space.