August  2013, 33(8): 3391-3405. doi: 10.3934/dcds.2013.33.3391

Optimal partial regularity results for nonlinear elliptic systems in Carnot groups

1. 

Department of Mathematics and Information Science, Zhangzhou Normal University, Zhangzhou 363000, Fujian, China

2. 

School of Mathematical Science, Xiamen University, Xiamen 361005, Fujian

Received  May 2012 Revised  July 2012 Published  January 2013

In this paper, we consider partial regularity for weak solutions of second-order nonlinear elliptic systems in Carnot groups. By the method of A-harmonic approximation, we establish optimal interior partial regularity of weak solutions to systems under controllable growth conditions with sub-quadratic growth in Carnot groups.
Citation: Shuhong Chen, Zhong Tan. Optimal partial regularity results for nonlinear elliptic systems in Carnot groups. Discrete & Continuous Dynamical Systems, 2013, 33 (8) : 3391-3405. doi: 10.3934/dcds.2013.33.3391
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show all references

References:
[1]

Seminaro Math. Scuola Norm. Sup. Pisa, 61(1960), Editrice Tecnico Scientifica, Pisa 57(1961).  Google Scholar

[2]

Boll.Un. Mat. Ital., 4 (1968), 135-137.  Google Scholar

[3]

J.Reine Angew. Math., 311-312 (1979), 145-169.  Google Scholar

[4]

Manus. Math., 30 (1979), 53-88. doi: 10.1007/BF01305990.  Google Scholar

[5]

Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat., 8 (2007), 63-81.  Google Scholar

[6]

Manus. Math., 123 (2007), 453-491. doi: 10.1007/s00229-007-0100-8.  Google Scholar

[7]

Canberra: Australian National University Press, 1983.  Google Scholar

[8]

Annals of Math., 95 (1972), 417-491.  Google Scholar

[9]

L.Simon, "Theorems on Regularity and Singularity of Energy Minimizing Maps,", Basel, ().  doi: 10.1007/978-3-0348-9193-6.  Google Scholar

[10]

J.Diff.Geom., 17 (1982), 307-335.  Google Scholar

[11]

J.Reine Angew. Math., 546 (2002), 73-138. doi: 10.1515/crll.2002.046.  Google Scholar

[12]

Manus. Math., 103 (2000), 267-298. doi: 10.1007/s002290070007.  Google Scholar

[13]

J. Math. Anal. Appl., 335 (2007), 20-42. doi: 10.1016/j.jmaa.2007.01.042.  Google Scholar

[14]

Discrete Cont Dyn-A, 27 (2010), 981-993. doi: 10.3934/dcds.2010.27.981.  Google Scholar

[15]

Ann. Mat. Pura Appl., 184 (2005), 421-448. doi: 10.1007/s10231-004-0117-5.  Google Scholar

[16]

Ann. Inst. Henri Poincaré, Anal. Non Linéaire, 21 (2004), 735-766. doi: 10.1016/j.anihpc.2003.09.003.  Google Scholar

[17]

Math. Ann., 313 (1999), 263-295. doi: 10.1007/s002080050261.  Google Scholar

[18]

J. Eur. Math. Soc., 5 (2003), 1-40. doi: 10.1007/s100970200043.  Google Scholar

[19]

p27. arXiv: math. AP/ 0502569. Google Scholar

[20]

Cacl Var Partial Dif., 32 (2008), 25-51. doi: 10.1007/s00526-007-0127-4.  Google Scholar

[21]

Nonlinear Anal., 72 (2010), 4162-4187. doi: 10.1016/j.na.2010.01.048.  Google Scholar

[22]

Ark. Mat., 13 (1975), 161-207.  Google Scholar

[23]

Duke Math. J., 53 (1986), 503-523. doi: 10.1215/S0012-7094-86-05329-9.  Google Scholar

[24]

Comm. Pure Appl. Math., 49 (1996), 1081-1144. doi: 10.1002/(SICI)1097-0312(199610)49:10<1081::AID-CPA3>3.0.CO;2-A.  Google Scholar

[25]

Ann. Mat. Pura Appl. IV. Ser., 175 (1998), 141-164. doi: 10.1007/BF01783679.  Google Scholar

[26]

J. Math. Anal. Appl., 140 (1989), 115-135. doi: 10.1016/0022-247X(89)90098-X.  Google Scholar

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