JournalsrsmupVol. 130pp. 169–202

Hölder Continuity for Sub-Elliptic Systems Under the Sub-Quadratic Controllable Growth in Carnot Groups

  • Jialin Wang

    Gannan Normal University, Ganzhou, Jiangxi, China
  • Dongni Liao

    Gannan Normal University, Ganzhou, Jiangxi, China
  • Zefeng Yu

    Gannan Normal University, Ganzhou, Jiangxi, China
Hölder Continuity for Sub-Elliptic Systems Under the Sub-Quadratic Controllable Growth in Carnot Groups cover
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Abstract

This paper is devoted to optimal partial regularity of weak solutions to nonlinear sub-elliptic systems for the case 1<m<21<m<2 under the controllable growth condition in Carnot groups. We begin with establishing a Sobolev-Poincaré type inequality for the function uHW1,m(Ω),RN)u\in HW^{1,m}(\Omega),\mathbb {R}^{N}) with m(1,2)m\in (1,2), and then partial regularity with optimal local Hölder exponent for horizontal gradients of weak solutions to the systems is established by using A{\mathcal A}-harmonic approximation technique.

Cite this article

Jialin Wang, Dongni Liao, Zefeng Yu, Hölder Continuity for Sub-Elliptic Systems Under the Sub-Quadratic Controllable Growth in Carnot Groups. Rend. Sem. Mat. Univ. Padova 130 (2013), pp. 169–202

DOI 10.4171/RSMUP/130-6