论文标题
与对称锥体障碍物的弹性图有关的评论
A remark on elastic graphs with the symmetric cone obstacle
论文作者
论文摘要
本文涉及单方面约束下对称图上定义的弹性能的变异问题。假设障碍函数满足对称锥条件，我们证明了（i）最小化器的唯一性，（ii）最小化器的规律性丧失，以及（iii）（iii）以障碍大小的方式对生存和最小化的不存在分类。作为应用程序，我们将障碍物问题的解决方案表征为相应的动态问题的平衡。
This paper is concerned with the variational problem for the elastic energy defined on symmetric graphs under the unilateral constraint. Assuming that the obstacle function satisfies the symmetric cone condition, we prove (i) uniqueness of minimizers, (ii) loss of regularity of minimizers, and give (iii) complete classification of existence and non-existence of minimizers in terms of the size of obstacle. As an application, we characterize the solution of the obstacle problem as equilibrium of the corresponding dynamical problem.
