Partial regularity in the interior for discontinuous inhomogeneous elliptic system with VMO-coefficients

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• 作者：Zhong Tan ; Yanzhen Wang ; Shuhong Chen
• 关键词：Discontinuous elliptic systems ; Controllable growth condition ; VMO ; condition ; Higher integrability ; Partial regularity
• 刊名：Annali di Matematica Pura ed Applicata (1923 -)
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：196
• 期：1
• 页码：85-105
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer Berlin Heidelberg
• ISSN：1618-1891
• 卷排序：196

文摘

In this paper, we are concerned with discontinuous elliptic problems with VMO-coefficients in divergence form under natural and controllable growth conditions. We obtain that the weak solution u is locally Hölder continuous besides a singular set by using \(\mathcal {A}\)-harmonic approximation, where the Hölder exponent \(\alpha \in (0,1)\).