论文标题
奇异双重解决方案的总差异最小化问题的错误估计值
Error estimates for total-variation regularized minimization problems with singular dual solutions
论文作者
论文摘要
使用crouzeix-raviart有限元元素的总变差正规化最小化问题的有限元近似值的最新准最佳误差估计需要存在Lipschitz连续的双重解决方案，这通常不给出。我们提供了分析证明，表明双重解决方案的Lipschitz连续性通常不是必需的。使用Lipschitz截断技术，我们得出了直接取决于给定双重解决方案的Sobolev规则性的错误估计。
Recent quasi-optimal error estimates for the finite element approximation of total-variation regularized minimization problems using the Crouzeix--Raviart finite element require the existence of a Lipschitz continuous dual solution, which is not generally given. We provide analytic proofs showing that the Lipschitz continuity of a dual solution is not necessary, in general. Using the Lipschitz truncation technique, we, in addition, derive error estimates that depend directly on the Sobolev regularity of a given dual solution.
