Removable singularities of \(\varvec{m}\) -Hessian equations

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• 作者：Hülya Car ; René Pröpper
• 关键词：Removable singularities ; Hessian equations ; Nonlinear elliptic PDE ; Hopf lemma
• 刊名：Nonlinear Differential Equations and Applications NoDEA
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：24
• 期：1
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Analysis;
• 出版者：Springer International Publishing
• ISSN：1420-9004
• 卷排序：24

文摘

In this paper we give a new, less restrictive condition for removability of singular sets, E, of smooth solutions to the m-Hessian equation (and also for more general fully nonlinear elliptic equations) in \(\Omega {\setminus } E\), \(\Omega \subset \mathbb R^n\). Besides the existence and regularity results for these equations, the proof only makes use of the classical elliptic theory, i.e. the classical maximum principles and a Hopf lemma.