线性椭圆问题系数的弱最优控制

椭圆PDEs的最优系数

Optimal coefficients for elliptic PDEs

本文研究了椭圆PDEs中通过优化弹性顺应性准则确定最优系数的问题，并探讨了其作为最优控制问题的扩展形式。

Solving an inverse elliptic coefficient problem by convex non-linear semidefinite programming

Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown coefficient function in an elliptic PDE is to be determined from partial knowledge of its solutions. This is usually a highly non-linear ill-posed inverse problem, for which unique reconstructability results, stability estimates and global convergence of numerical methods are very hard to achieve. The aim of this note is to point out a new connection between inverse coefficient problems and semidefinite programming that may help addressing these challenge…

用于带精确数据的离散椭圆逆系数问题的完全全局化求解器

A fully globalized solver for discretized inverse elliptic coefficient problems with exact data

针对带精确数据的离散椭圆逆系数问题，研究人员开发了带显式残差准则的局部收敛算法及全局化变体，后者可在有限次全局搜索后切换至局部收敛算法，解决了数值求解器依赖良好初始值的问题。

完全非线性退化椭圆型方程的内部正则性I：常系数Bellman方程

Interior regularity of fully nonlinear degenerate elliptic equations, I: Bellman equations with constant coefficients

这是关于完全非线性退化椭圆型方程的内部正则性的一系列论文中的第一篇。考虑一类扩散系数、漂移系数和折扣因子与空间变量无关的随机最优控制问题。在适当的假设下，对于$k=0,1$，当终端支付和运行支付都是全局$C^{k,1}$时，我们得到了值函数的$C^{k,1}$ -光滑性，从而得到了退化Bellman方程的相关狄利克雷问题解的存在唯一性.