OPTIMAL PARTIAL REGULARITY FOR NONLINEAR SUB-ELLIPTIC SYSTEMS RELATED TO HORMANDER’S VECTOR FIELDS

摘要

This paper is concerned with partial regularity for weak solutions to nonlinear sub-elliptic systems related to Hormander’s vector fields. The method of A-harmonic approximation introduced by Simon and developed by Duzaar and Grotowski is adapted to our context, and then a Caccioppoli-type inequality and partial regularity with optimal local Holder exponent for gradients of weak solutions to the systems under super-quadratic natural growth conditions is established.