Lp ESTIMATES FOR WEAK SOLUTIONS TO NONLINEAR SUB-ELLIPTIC SYSTEMS RELATED TO HÖRMANDER'S VECTOR FIELDS

Jialin WANG, Pengcheng NIU, Xuewei CUI
2009 Kyushu Journal of Mathematics  
This paper is concerned with the regularity of weak solutions to the general nonlinear sub-elliptic systems related to Hörmander's vector fields. Based on the reverse Hölder inequality established by Gianazza, the L p estimates for weak solutions to the systems under the super-quadratic controllable growth condition and the natural growth condition are established, respectively. Then we obtain the Hölder continuity for weak solutions.
doi:10.2206/kyushujm.63.301 fatcat:dgqh3rsuarfx5hefn7ee66fspu