论文标题
Carnot组的某些退化椭圆方程的经典解决方案的平均值公式
Mean value formulas for classical solutions to some degenerate elliptic equations in Carnot groups
论文作者
论文摘要
我们证明了与Hölder连续系数以差异形式均匀椭圆方程的经典解的表面和体积平均值公式。在积分中出现的内核在基本解决方案的级别和超级集合中支持与伴随差分运算符相关。然后，我们将上述公式扩展到Carnot组的某些次小额算子。在这种情况下，我们依靠有限周长的理论对分层的谎言组。
We prove surface and volume mean value formulas for classical solutions to uniformly elliptic equations in divergence form with Hölder continuous coefficients. The kernels appearing in the integrals are supported on the level and superlevel sets of the fundamental solution relevant the adjoint differential operator. We then extend the aforementioned formulas to some subelliptic operators on Carnot groups. In this case we rely on the theory of finite perimeters on stratified Lie groups.
