Monge-Ampere type equations and their applications

Monge-Ampere型方程及其应用

• 批准号: FT220100368
• 负责人: A/Prof Jiakun Liu
• 金额: $ 65.02万
• 依托单位: University of Wollongong
• 依托单位国家: 澳大利亚
• 项目类别: ARC Future Fellowships
• 财政年份: 2023
• 资助国家: 澳大利亚
• 起止时间: 2023-06-26 至 2027-06-25
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/FT220100368
• 关键词: Monge; Ampere; type; equations; their

The study of Monge-Ampere equations has attracted major attention in mathematics in recent years, due to many significant applications in geometry, physics and applied science. This project aims to resolve challenging problems involving Monge-Ampere type equations, by utilising new ideas and breakthroughs made by the proposer. A comprehensive regularity theory for Monge-Ampere type equations, particularly in the degenerate case, is expected to be established. Innovative cutting-edge techniques and interdisciplinary approaches are expected to be developed. Anticipated outcomes of this project include the resolution of outstanding open problems and continuing enhancement of Australian leadership and expertise in a major area of mathematics.

由于几何，物理学和应用科学中的许多重要应用，近年来对Monge-Ampere方程的研究引起了数学的主要关注。该项目旨在通过利用提议者的新想法和突破来解决涉及Monge-Ampere类型方程的具有挑战性的问题。预计将建立针对Monge-Ampere类型方程的综合规则理论，特别是在退化情况下。预计将开发创新的尖端技术和跨学科方法。该项目的预期结果包括解决杰出的开放问题以及在主要数学领域的澳大利亚领导力和专业知识的持续增强。