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Monge-Ampere方程在几何、物理和应用科学中的重要应用，近年来，Monge-Ampere方程的研究引起了数学界的极大关注。该项目旨在通过利用提出者的新思想和突破来解决涉及Monge-Ampere类型方程的挑战性问题。Monge-Ampere型方程的正则性理论，特别是在退化的情况下，有望建立。预计将开发创新的尖端技术和跨学科方法。该项目的预期成果包括解决悬而未决的问题，并继续加强澳大利亚在数学的一个主要领域的领导地位和专业知识。