| In this paper,we mainly consider nonlinear sub-elliptic and parabolic systems in divergence form,in the Heisenberg group.Under assumptions of different growth conditions,H (?)lder continuity results of weak solutions are established.The details are given as follows.The first chapter briefly introduces the research background and progress of sub-elliptic systems,and the research contents,methods and innovations of this paper.The second chapter focuses on introducing preliminaries of the paper,including introductions of the Heisenberg group,the horizontal affine functions and several estimates,function spaces and its embedding theorems.In the third chapter,we study nonlinear sub-elliptic systems with VMO-coefficients in the Heisenberg group.By using the technique of A-harmonic approximation,we obtain optimal partial H (?)lder continuity of weak solutions to the sub-elliptic systems under the sub-quadratic growth conditions.In the fourth chapter,we consider nonlinear sub-elliptic parabolic systems in the Heisenbeg groups.On the basis of the method of A-caloric approximation,we establish H (?)lder continuity for weak solutions under super-quadratic growth conditions. |
