Mathematical Sciences: "Nonlinear partial differential equations and systems"

这个项目将研究由多重对称积分导出的椭圆方程的解。重点讨论了拟凸性和秩凸性之间的关系、拟凸性和秩凸性之间的关系、拟凸性的边界估计、全局正则性、孤立和可去除的奇点、先验梯度估计。所研究的方程模拟了几何、优化设计和非线性弹性中的现象。因此，该项目在数学和工程的各个分支中都有应用。

This project will study solutions to elliptic equations derived from multiple integrals with symmetries. The topics to be emphasized are estimates up to the boundary, global regularity, isolated and removable singularities, apriori gradient estimates, and the relation between quasiconvexity and rank one convexity. The equations to be studied model phenomena in geometry, optimal design and nonlinear elasticity. Thus this project has applications in various branches of mathematics and engineering.