High Order Fefferman-Phong Type Inequalities in Carnot Groups and Regularity for Degenerate Elliptic Operators plus a Potential
Let {X1,X2,…,Xm} be the basis of space of horizontal vector fields in a Carnot group G=(Rn;∘) (m<n). We prove high order Fefferman-Phong type inequalities in G. As applications, we derive a priori Lp(G) estimates for the nondivergence degenerate elliptic operators L=-∑i,j=1maij(x)XiXj+V(x) with V...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/274859 |
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| Summary: | Let {X1,X2,…,Xm} be the basis of space of horizontal vector fields in a Carnot group G=(Rn;∘) (m<n). We prove high order Fefferman-Phong type inequalities in G. As applications, we derive a priori Lp(G) estimates for the nondivergence degenerate elliptic operators L=-∑i,j=1maij(x)XiXj+V(x) with VMO coefficients and a potential V 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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| ISSN: | 1085-3375 1687-0409 |