Parabolic methods for elliptic boundary value problems

本项目旨在利用相关的非线性抛物型偏微分方程解的唯一性来揭示二阶非线性椭圆型偏微分方程解的新结果。这将建立在过去30年发展起来的完全非线性方程的理论基础上。该项目预计将在理论方面产生新的知识，这些知识将指导未来的研究，并对最优交通、几何问题以及图像分析和数学金融等更多应用领域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。

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.