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

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  • Pengcheng Niu
  • Kelei Zhang

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.

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  • Pengcheng Niu & Kelei Zhang, 2014. "High Order Fefferman-Phong Type Inequalities in Carnot Groups and Regularity for Degenerate Elliptic Operators plus a Potential," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, November.
    • Handle: RePEc:hin:jnlaaa:274859
    DOI: 10.1155/2014/274859
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