Heisenberg群上退化椭圆方程组的最优Hlder正则性

Optimal Partial Hlder Regularity for Sub-elliptic Systems in Heisenberg Groups

利用新方法—A-调和逼近技巧,研究Heisenberg群上非线性次椭圆方程组在自然增长条件下弱解的Hlder正则性,得到弱解的局部Γ1,α估计.该方法避免了反向Hlder不等式的建立和应用,且由此建立的Hlder指标是最优的.

This paper is concerned with the partial Holder regularity for nonlinear sub-elliptic systems under the natural growth condition in Heisenberg groups.Based on a new method,the technique of A-harmonic approximation,the local estimate of weak solutions is obtained.The approach avoids establishing and applying the reverse Holder inequality.Particularly,the optimal Holder exponent is established directly.