一类凸化方程的指数收敛性和全局极小化的非自治梯度流
Exponential convergence for a convexifying equation and a non-autonomous gradient flow for global minimization
摘要：
我们考虑一个类似于Vese提出的发展方程，其解在大时间内收敛于初始数据的凸包络。我们给出了一个随机控制表示的解决方案，从中我们推断，在相当一般的假设下，收敛的Lipschitz范数实际上是指数的时间。然后，我们引入一个非自治梯度流，并证明其轨迹都收敛到凸包络的极小。
英文摘要：
We consider an evolution equation similar to that introduced by Vese and whose solution converges in large time to the convex envelope of the initial datum. We give a stochastic control representation for the solution from which we deduce, under quite general assumptions that the convergence in the Lipschitz norm is in fact exponential in time. We then introduce a non-autonomous gradient flow and prove that its trajectories all converge to minimizers of the convex envelope.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
