Abstract and Applied Analysis

Partial Regularity for Nonlinear Subelliptic Systems with Dini Continuous Coefficients in Heisenberg Groups

Jialin Wang, Pingzhou Hong, Dongni Liao, and Zefeng Yu

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Abstract

This paper is concerned with partial regularity to nonlinear subelliptic systems with Dini continuous coefficients under quadratic controllable growth conditions in the Heisenberg group n . Based on a generalization of the technique of 𝒜 -harmonic approximation introduced by Duzaar and Steffen, partial regularity to the sub-elliptic system is established in the Heisenberg group. Our result is optimal in the sense that in the case of Hölder continuous coefficients we establish the optimal Hölder exponent for the horizontal gradients of the weak solution on its regular set.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 950134, 12 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393512072

Digital Object Identifier
doi:10.1155/2013/950134

Mathematical Reviews number (MathSciNet)
MR3108667

Zentralblatt MATH identifier
07095529

Citation

Wang, Jialin; Hong, Pingzhou; Liao, Dongni; Yu, Zefeng. Partial Regularity for Nonlinear Subelliptic Systems with Dini Continuous Coefficients in Heisenberg Groups. Abstr. Appl. Anal. 2013 (2013), Article ID 950134, 12 pages. doi:10.1155/2013/950134. https://projecteuclid.org/euclid.aaa/1393512072


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