SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1857-1885, January 2021.
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 and (ii) loss of regularity of minimizers and give (iii) complete classification of existence and nonexistence of minimizers in terms of the size of obstacle. As an application, we characterize the solution of obstacle problem as equilibrium of the corresponding dynamical problem.

中文翻译：

---

关于具有对称圆锥形障碍的弹性图的一个注记

SIAM数学分析期刊，第53卷，第2期，第1857-1885页，2021年1月。
本文涉及在单边约束下对称图上定义的弹性能的变分问题。假设障碍函数满足对称圆锥条件，我们证明（i）最小化器的唯一性和（ii）最小化器规则性的损失，并（iii）根据障碍物的大小对存在和不存在最小化器进行完整的分类。作为应用，我们将障碍问题的解决方案描述为相应动力学问题的平衡。