Gradient potential estimates in non-linear elliptic obstacle problems with measure data
Gradient potential estimates in non-linear elliptic obstacle problems with measure data
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DOI：
10.1016/j.jfa.2012.01.003
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发表时间：
2012-03
影响因子：
1.7
通讯作者：
Christoph Scheven
中科院分区：
文献类型：
--
作者：
Christoph Scheven
本文给出了具有测度数据的p-Laplace型椭圆障碍问题解的梯度的逐点估计。此外，我们还讨论了正则性理论中的一个边界问题，并给出了一个判别解的梯度连续性的精确准则。其他的应用是梯度的Lorentz空间估计和解的C1，α-正则性的判据。
In this paper, we derive pointwise estimates for the gradients of solutions to elliptic obstacle problems of p-Laplace-type with measure data. Moreover, we address a borderline problem in the regularity theory and give a sharp criterion for continuity of the gradient of a solution. Other applications are Lorentz space estimates for the gradient and a criterion for C1,α-regularity of solutions.