Gradient Continuity for Nonlinear Obstacle Problems

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• 作者：Jihoon Ok
• 关键词：Obstacle problem ; variational inequality ; gradient continuity ; Dini continuity
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：14
• 期：1
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1660-5454
• 卷排序：14

文摘

We prove that the gradients of solutions to obstacle problems are continuous if the gradients of obstacles satisfy a Dini type continuity assumption. We also consider coefficients and nonhomogeneous data and investigate their regularity conditions to obtain gradient continuity, extending to the constrained case results starting with those presented by Mingione (J Eur Math Soc 13:459–486, 2011).