SONG Qiao-Zhen , WANG Li-He , LI Dong-Sheng . HÖLDER ESTIMATES FOR A CLASS OF DEGENERATE ELLIPTIC EQUATIONS[J]. Acta mathematica scientia, Series B, 2013 , 33(4) : 1202 -1218 . DOI: 10.1016/S0252-9602(13)60074-0

[1] Chen G S. Tight embeddings and projective transformations. Amer J Math, 1979, 101(5): 1083–1102

[1] H¨ormander L. Hypoelliptic second order differential equations. Acta Math, 1967, 119: 147–171

[2] Jerison D. The Poincar´e inequality for vector fields satisfying H¨ormander´s condition. Duke Math J, 1986, 53: 503–523

[3] S´anchez-Calle A. Fundamental solutions and geometry of the sum of squares of vector fields. Invent Math, 1984, 78: 143–160

[4] Kohn JJ. Pseudo differential operators and hypoellipticity. Prec Symp Pure Math, Amer Math Soc, 1973, 23: 61–69

[5] Rothschild LP, Stein EM. Hypoelliptic differential operator and nilpotent groups. Acta Math, 1977, 137: 247–320

[6] Xu C. An existence result for a class of semilinear degenetate elliptic equations. Adv Math (China), 1996, 25: 492–499

[7] Xu C. Existence of bounded solutions for quasilinear subelliptic Dirichlet problems. J Partial Diff Eqs, 1995, 8: 97–107

[8] Xu C, Zuily C. Highter interior regularity for quasilinear subelliptic systems. Calc Var, 1997, 5: 323–343

[9] Xu C. Regularity for quasilinear second-order subelliptic equations. Comm Pure Appl Math, 1992, 45: 77–96

[10] Xu C. The Dirichlet problems for a class of semilinear sub-elliptic equations. Nonlinear Analysis, 1999, 37: 1039–1049

[11] Xu C. Subelliptic variational problems. Bull Soc Math France, 1990, 118: 147–169

[12] Murthy M K V. A class of subelliptic quasilinear equations. J Glob Optim, 2008, 40: 245–260

[13] Berhanu S, Pesenson I. The trace problem for vector fields satisfying H¨ormander´s condition. Math Z, 1999, 231: 103–122

[14] Lanconelli E, Morbidelli D. On the Poincar´e inequality for the vector fields. Ark Mat, 2000, 38: 327–342

[15] Montanari A, Morbidelli D. Balls defined by nonsmooth vector fields and the Poincar´e inequality. Ann Inst Fourier, 2004, 54(2): 431–452

[16] Franchi B, Lanconelli E. H¨older regularity theorem for a class of linear nonuniformly elliptic operator with
measurable coefficients. Ann Scuola Norm Sup Pisa, 1983, 10(4): 523–541

[17] Franchi B, Serapioni R. Pointwise estimates for a class of strongly degenerate elliptic operators: a geometrical
approach. Ann Scuola Norm Sup Pisa, 1987, 14(4): 527–568

[18] Wang L. H¨older estimates for subelliptic opertors. J Funct Anal, 2003, 199: 228–242

[19] Franchi B. Weighted Sobolev-Poincar´e inequalities and pointwise estimates for a class of degenerate elliptic
equations. Trans Amer Math Soc, 1991, 327: 125–158

[20] Fazio GD, Zamboni P. H¨older continuity for quasilinear subelliptic equations in Carnot Carath´eodory spaces. Math Nachr, 2004, 272: 3–10

[21] Li K, Wei H. Infinitely many solutions for a class of degenerate elliptic equations. Acta Math Sci, 2011, 31B(5): 1899–1910

[22] Zhang L, Zhao J. Existence and uniqueness of renormalized solutions for a class of degenerate parabolic equations. Acta Math Sci, 2009, 29B(2): 251–264

[23] Wen G. Some boundary value problems for nonlinear degenerate elliptic equations of second order. Acta Math Sci, 2007, 27B(3): 663–672

[24] Xu C J. The Harnack’s inequality for second order degenerate elliptic operators. Chinese Ann Math Ser A, 1989 10: 359–365

[25] Byun S S, Wang L. Elliptic Equations with BMO coefficents in Refinberg domains. Comm Pure Appl Math, 2004, 57: 1283–1310

[26] Caffarelli L A, Peral I. On W1,p estimates for elliptic equations in divergence form. Comm Pure Appl Math, 1996, 49: 1081–1144