Optimal partial regularity results for nonlinear elliptic systems in Carnot groups

Shuhong Chen; Zhong Tan

doi:10.3934/dcds.2013.33.3391

Article Contents

2013, Volume 33, Issue 8: 3391-3405. Doi: 10.3934/dcds.2013.33.3391

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Optimal partial regularity results for nonlinear elliptic systems in Carnot groups

Shuhong Chen^1, and
Zhong Tan^2,

1.
Department of Mathematics and Information Science, Zhangzhou Normal University, Zhangzhou 363000, Fujian
2.
School of Mathematical Science, Xiamen University, Xiamen 361005, Fujian

Received: April 30, 2012

Revised: June 30, 2012

Published: July 2013

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Abstract

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.

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Mathematics Subject Classification: Primary: 35B65, 35J47; Secondary: 35J60.

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