奇异Monge-Ampère方程粘性解的广义Liouville定理

IF 3.2 1区数学 Q1 MATHEMATICS Advances in Nonlinear Analysis Pub Date : 2023-01-01 DOI:10.1515/anona-2022-0284

H. Jian, Xianduo Wang

{"title":"奇异Monge-Ampère方程粘性解的广义Liouville定理","authors":"H. Jian, Xianduo Wang","doi":"10.1515/anona-2022-0284","DOIUrl":null,"url":null,"abstract":"Abstract In this article, we study the asymptotic behaviour at infinity for viscosity solutions to a singular Monge-Ampère equation in half space from affine geometry. In particular, we extend the Liouville theorem for smooth solutions to the case of viscosity solutions by a completely different method from the smooth case.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":" ","pages":""},"PeriodicalIF":3.2000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Generalized Liouville theorem for viscosity solutions to a singular Monge-Ampère equation\",\"authors\":\"H. Jian, Xianduo Wang\",\"doi\":\"10.1515/anona-2022-0284\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this article, we study the asymptotic behaviour at infinity for viscosity solutions to a singular Monge-Ampère equation in half space from affine geometry. In particular, we extend the Liouville theorem for smooth solutions to the case of viscosity solutions by a completely different method from the smooth case.\",\"PeriodicalId\":51301,\"journal\":{\"name\":\"Advances in Nonlinear Analysis\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":3.2000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Nonlinear Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/anona-2022-0284\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Nonlinear Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/anona-2022-0284","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

摘要在本文中，我们从仿射几何的角度研究了半空间中奇异Monge-Ampère方程粘性解在无穷大处的渐近行为。特别地，我们用与光滑情况完全不同的方法将光滑解的刘维尔定理推广到粘性解的情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Generalized Liouville theorem for viscosity solutions to a singular Monge-Ampère equation

Abstract In this article, we study the asymptotic behaviour at infinity for viscosity solutions to a singular Monge-Ampère equation in half space from affine geometry. In particular, we extend the Liouville theorem for smooth solutions to the case of viscosity solutions by a completely different method from the smooth case.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Advances in Nonlinear Analysis MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

6.00

自引率

9.50%

发文量

审稿时长

30 weeks

期刊介绍： Advances in Nonlinear Analysis (ANONA) aims to publish selected research contributions devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The Journal focuses on papers that address significant problems in pure and applied nonlinear analysis. ANONA seeks to present the most significant advances in this field to a wide readership, including researchers and graduate students in mathematics, physics, and engineering.