Regularity of subelliptic p-harmonic systems with subcritical growth in Carnot group

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:258

Article

Zheng, Shenzhou¹  Feng, Zhaosheng² 

[1] Beijing Jiaotong Univ, Dept Math, Beijing 100044, Peoples R China

[2] Univ Texas Pan Amer, Dept Math, Edinburg, TX 78539 USA

关键词: p-harmonic system;    Interior regularity;    Weak solution;    Maximum principle;    Money's space;    Interior Holder continuity;   

DOI  :  10.1016/j.jde.2014.12.020

来源: Elsevier

【 摘 要 】

For a class of subelliptic p-harmonic systems with the subcritical growth defined in Carnot groups, we prove that the weak solutions belong to Gamma(1,alpha)(loc)-regularity with respect to the Carnot-Caratheodory distance provided that p is close to 2. As a consequence, we make it clear that the critical growth of nonlinearity for p-harmonic type systems in Carnot groups is just a sharp borderline of partial regularity of the small excess energy due to the counterexamples of p-harmonic maps with p close to 2. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free