Partial regularity for degenerate subelliptic systems associated with Hörmander’s vector fields

Nonlinear Analysis, Theory, Methods and Applications - Tập 73 - Trang 3209-3223 - 2010
Dan Gao1, Pengcheng Niu1, Jialin Wang2
1Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, Shaanxi, PR China
2College of Mathematics and Computer Science, Gannan Normal University, Ganzhou, 341000, Jiangxi, PR China

Tài liệu tham khảo

De Giorgi, 1968, Un esempio di estremali discontinue per un problema variazionale di tipo ellittico, Boll. Unione. Mat. Ital., 4, 135

S. Campanato, Sistemi ellittici in forma di divergenza, Regolarita’all’interno, Quaderni Scuola Norm. Pisa, 1980.

Chen, 2003

Duzaar, 2002, Optimal interior and boundary regularity for almost minimizers to elliptic variational integrals, J. Reine Angew. Math., 546, 73, 10.1515/crll.2002.046

Zheng, 2008, Partial regualrity for quasilinear elliptic systems with VMO coefficients under natural growth condition, Chin. Ann. Math., 29, 49

Giaquinta, 1983

Capogna, 1997, Regularity of quasi-linear equations in the Heisenberg group, Comm. Pure Appl. Math., 50, 867, 10.1002/(SICI)1097-0312(199709)50:9<867::AID-CPA3>3.0.CO;2-3

Capogna, 1993, An embedding theorem and the Harnack inequality for nonlinear subelliptic equations, Comm. Partial Differential Equations, 18, 1765, 10.1080/03605309308820992

Lu, 1996, Embedding theorems into Lipschitz and BMO spaces and applications to quasilinear subelliptic differential equations, Publ. Mat., 40, 301, 10.5565/PUBLMAT_40296_04

Wang, 2009, Lp estimates for weak solutions to nonlinear subelliptic systems related to Hörmander’s vector fields, Kyushu J. Math., 63, 301, 10.2206/kyushujm.63.301

Ragusa, 2008, Regularity of minimizers of some variational integrals with discontinuity, Z. Anal. Anwend., 27, 469, 10.4171/ZAA/1366

Föglein, 2008, Partial regularity results for subelliptic systems in the Heisenberg group, Calc. Var. Partial Differential Equations, 32, 25, 10.1007/s00526-007-0127-4

Rothschild, 1977, Hypoelliptic operators and nilpotent Lie groups, Acta Math., 137, 247, 10.1007/BF02392419

Gianazza, 1994, Regularity for non-linear equations involving square Hörmander operators, Nonlinear Anal. TMA, 23, 49, 10.1016/0362-546X(94)90251-8

Nagel, 1985, Balls and metrics defined by vector fields I: basic properties, Acta Math., 155, 130, 10.1007/BF02392539

Chiarenza, 1993, W2,p solvability of the Dirichlet problem for nonlinear elliptic equations with VMO coefficients, Trans. Amer. Math. Soc., 336, 841, 10.2307/2154379

Wu, 2003

Zheng, 2008, Regularity for a class of degenerate elliptic equations with discontinuous coefficients under natural growth, J. Math. Anal. Appl., 346, 359, 10.1016/j.jmaa.2008.05.059

Garofalo, 1996, Isoperimetric and Sobolev inequalities for Carnot–Carathéodery spaces and the existence of minimal surfaces, Comm. Pure Appl. Math., 10, 1081, 10.1002/(SICI)1097-0312(199610)49:10<1081::AID-CPA3>3.0.CO;2-A

Jerison, 1986, The Poincaré inequality for vector fields satisfying Hörmander’s condition, Duke Math. J., 53, 503, 10.1215/S0012-7094-86-05329-9

Lu, 1992, Weighted Poincaré and Sobolev inequalities for vector fields satisfying Hörmander’s condition, Rev. Mat. Iberoam., 8, 367, 10.4171/RMI/129

Franchi, 2005, Homogenization and convergence of correctors in Carnot groups, Comm. Partial Differential Equations, 30, 1817, 10.1080/03605300500300014

Zhou, 2001, A generalization of Lebesgue differential theorem and its application, Acta Math. Sci., 21, 109, 10.1016/S0252-9602(17)30583-0

Bramanti, 1994, Commutators of integral operators with positive kernels, Matematiche (Catania), 49, 149

Ziemer, 1989