Estimates in Morrey Spaces and Hölder Continuity for Weak Solutions to Degenerate Elliptic Systems
Estimates in Morrey Spaces and Hölder Continuity for Weak Solutions to Degenerate Elliptic Systems
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DOI：
10.1007/s00229-011-0498-x
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发表时间：
2011-10
影响因子：
0.6
通讯作者：
Yan Dong;P. Niu
中科院分区：
文献类型：
--
作者：
Yan Dong;P. Niu
本文在Morrey空间和Hölder连续性中建立了下列退化椭圆型方程组弱解的梯度估计，其中X，…，X是满足Hörmander条件的真实的光滑向量场，系数$${a_ {ij}^{\alpha\beta}\in VMO_X\cap L^\infty（\Omega），\alpha，\beta= 1，2，\，.\，，q，i，j= 1，2，\，.\，N，X_ {\alpha}^{\ast}}$$是X的转置向量场。
In this paper, we establish gradient estimates in Morrey spaces and Hölder continuity for weak solutions of the following degenerate elliptic system where X,..., X are real smooth vector fields satisfying Hörmander's condition, coefficients $${a_ {ij}^{\alpha\beta}\in VMO_X\cap L^\infty (\Omega),\alpha,\beta= 1, 2,\,.\,.\,.\,, q, i, j= 1, 2,\,.\,.\,.\,, N, X_ {\alpha}^{\ast}} $$ is the transposed vector field of X.