Parabolic methods for elliptic boundary value problems

椭圆边值问题的抛物线方法

• 批准号: DP180100431
• 负责人: Prof James McCoy
• 金额: $ 20.78万
• 依托单位: The University of Newcastle
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2018
• 资助国家: 澳大利亚
• 起止时间: 2018-08-01 至 2024-05-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP180100431
• 关键词: Parabolic; methods; elliptic; boundary; value

This project aims to uncover new results for second order nonlinear elliptic partial differential equations via the use of uniqueness properties of solutions for related nonlinear parabolic partial differential equations. This will build on theory for fully nonlinear equations developed over the last 30 years. The project expects to generate new knowledge in the theory that will guide future research and have direct impact to applications in optimal transport, geometric problems and more applied areas including image analysis and mathematical finance. The project will enhance Australia's international reputation for research in the field and train some of the next generation of mathematical analysts.

本项目旨在利用相关非线性抛物型偏微分方程解的唯一性性质，揭示二阶非线性椭圆型偏微分方程的新结果。 这将建立在过去30年来发展的完全非线性方程的理论基础上。该项目预计将在理论中产生新的知识，这些知识将指导未来的研究，并对最佳运输，几何问题和更多应用领域（包括图像分析和数学金融）的应用产生直接影响。该项目将提高澳大利亚在该领域研究的国际声誉，并培养一些下一代数学分析师。