Global Lipschitz continuity for minima of degenerate problems

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• 作者：Pierre Bousquet ; Lorenzo Brasco
• 关键词：Mathematics Subject Classification49N60 ; 49K20 ; 35B65
• 刊名：Mathematische Annalen
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：366
• 期：3-4
• 页码：1403-1450
• 全文大小：1,044 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1807
• 卷排序：366

文摘

We consider the problem of minimizing the Lagrangian \(\int [F(\nabla u)+f\,u]\) among functions on \(\Omega \subset \mathbb {R}^N\) with given boundary datum \(\varphi \). We prove Lipschitz regularity up to the boundary for solutions of this problem, provided \(\Omega \) is convex and \(\varphi \) satisfies the bounded slope condition. The convex function F is required to satisfy a qualified form of uniform convexity only outside a ball and no growth assumptions are made.