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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1849306864939958272 |
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| author | Pengcheng Niu Kelei Zhang |
| author_facet | Pengcheng Niu Kelei Zhang |
| author_sort | Pengcheng Niu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-20d035b8574447e899b09239327ea8ed |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-20d035b8574447e899b09239327ea8ed2025-08-20T03:54:57ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/274859274859High Order Fefferman-Phong Type Inequalities in Carnot Groups and Regularity for Degenerate Elliptic Operators plus a PotentialPengcheng Niu0Kelei Zhang1Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi 710129, ChinaDepartment of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi 710129, ChinaLet {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.http://dx.doi.org/10.1155/2014/274859 |
| spellingShingle | Pengcheng Niu Kelei Zhang High Order Fefferman-Phong Type Inequalities in Carnot Groups and Regularity for Degenerate Elliptic Operators plus a Potential Abstract and Applied Analysis |
| title | High Order Fefferman-Phong Type Inequalities in Carnot Groups and Regularity for Degenerate Elliptic Operators plus a Potential |
| title_full | High Order Fefferman-Phong Type Inequalities in Carnot Groups and Regularity for Degenerate Elliptic Operators plus a Potential |
| title_fullStr | High Order Fefferman-Phong Type Inequalities in Carnot Groups and Regularity for Degenerate Elliptic Operators plus a Potential |
| title_full_unstemmed | High Order Fefferman-Phong Type Inequalities in Carnot Groups and Regularity for Degenerate Elliptic Operators plus a Potential |
| title_short | High Order Fefferman-Phong Type Inequalities in Carnot Groups and Regularity for Degenerate Elliptic Operators plus a Potential |
| title_sort | high order fefferman phong type inequalities in carnot groups and regularity for degenerate elliptic operators plus a potential |
| url | http://dx.doi.org/10.1155/2014/274859 |
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