Matrix $A_p$ weights, degenerate Sobolev spaces, and mappings of finite distortion.
Matrix $A_p$ weights, degenerate Sobolev spaces, and mappings of finite distortion.
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矩阵 $A_p$ 权重、简并 Sobolev 空间和有限失真映射。
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发表时间：
2015
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通讯作者：
S. Rodney
中科院分区：
文献类型：
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作者：
D. Cruz;Kabe Moen;S. Rodney
本文研究了退化的Sobolev空间，其中退化由矩阵$A_p$权控制.这类权是由Nazarov，Treil和Volberg引入的，而具有矩阵权的退化Sobolev空间已经被几位作者考虑应用于偏微分方程。我们证明了经典的Meyers-Serrin定理，H = W，在此设置。作为应用，我们证明了退化p-Laplacian方程弱解的部分正则性结果，特别是有限畸变映射。
We study degenerate Sobolev spaces where the degeneracy is controlled by a matrix $A_p$ weight. This class of weights was introduced by Nazarov, Treil and Volberg, and degenerate Sobolev spaces with matrix weights have been considered by several authors for their applications to PDEs. We prove that the classical Meyers-Serrin theorem, H = W, holds in this setting. As applications we prove partial regularity results for weak solutions of degenerate p-Laplacian equations, and in particular for mappings of finite distortion.