\({{\varvec{W}}}^{{\varvec{1,p}}}_{\varvec{\varphi }}\) -estimates for Green’s functions of the linearized Monge–Ampère operator

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• 作者：Diego Maldonado
• 关键词：Mathematics Subject ClassificationPrimary 35J08 ; 35J96 ; Secondary 35J70 ; 35J75
• 刊名：manuscripta mathematica
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：152
• 期：3-4
• 页码：539-554
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general; Algebraic Geometry; Topological Groups, Lie Groups; Geometry; Number Theory; Calculus of Variations and Optimal Control; Optimization;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-1785
• 卷排序：152

文摘

It is proved that Green’s functions associated to the linearized Monge–Ampère operator satisfy certain Sobolev-type estimates within the natural first-order calculus. Our main result extends the classical Sobolev estimates for Green’s functions due to Grüter and Widman (Manuscr Math 37(3):303–342, 1982) in the uniformly elliptic case and it addresses a question posed by Le (Manuscr Math 149:45–62, 2016) in the degenerate and/or singular Monge–Ampère setting.