This paper is devoted to optimal partial regularity of weak solutions to nonlinear sub-elliptic systems for the case under the controllable growth condition in Carnot groups. We begin with establishing a Sobolev-Poincaré type inequality for the function with , and then partial regularity with optimal local Hölder exponent for horizontal gradients of weak solutions to the systems is established by using -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. 169–202DOI 10.4171/RSMUP/130-6