Carnot群上散度型退化椭圆方程组的内Morrey估计(英文)

Interior Morrey estimates for divergence degenerate elliptic systems in Carnot groups

设X1,…,X q是Carnot群G=(Rn,o)(q<n)上的一组水平向量场的基.主要考虑下面的散度型退化方程组N∑β=1q∑i,j=1Xi(aijαβ(x)Xjuβ)=q∑i=1Xifαi,α=1,2,…,N,其中,系数aijαβ是ΩG上的实的有界VMO loc(Ω)函数并且满足强Legendre条件.得到该方程组弱解的内Morrey估计.

Let X1 , ..., Xq be the basis of the space of horizontal vector fields on a homogeneous Carnot group G = （ Rn ,o） （q 〈 n）. The interior Morrey estimates for weak solutions to the following divergence degenerate elliptic system β=1∑Ni,j=1∑qXi（aαβ^ij（x）Xjuβ）=i=1∑qXifiα,α=1,2,…,N are obtained when the coefficients aαβ^ij satisfy the strong Legendre condition in Ω G and belong to the space VMOloc （Ω）.