论文标题
P弹性能量的障碍问题
An obstacle problem for the p-elastic energy
论文作者
论文摘要
在本文中，我们考虑了在具有固定末端的图形曲线中P弹性能概括的障碍问题。考虑到Euler-Lagrange方程具有堕落，我们解决了一个问题，解决方案是否具有平坦的部分，即曲率消失的开放时间间隔。我们还调查了哪些是丧失规律性，障碍或堕落的主要原因。此外，我们给出了确保解决方案存在和不存在的障碍的几个条件。该分析可以在P-Elastica功能的特殊情况下进行完善，在那里我们获得了鲜明的存在结果和对称最小化器的独特性。
In this paper we consider an obstacle problem for a generalization of the p-elastic energy among graphical curves with fixed ends. Taking into account that the Euler--Lagrange equation has a degeneracy, we address the question whether solutions have a flat part, i.e. an open interval where the curvature vanishes. We also investigate which is the main cause of the loss of regularity, the obstacle or the degeneracy. Moreover, we give several conditions on the obstacle that assure existence and nonexistence of solutions. The analysis can be refined in the special case of the p-elastica functional, where we obtain sharp existence results and uniqueness for symmetric minimizers.
