An obstacle problem for the p-elastic energy

Autor:	Dall'Acqua, Anna, Müller, Marius, Okabe, Shinya, Yoshizawa, Kensuke
Rok vydání:	2022
Předmět:	Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
Popis:	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. Comment: 42 pages, 5 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2202.09893 Zobrazit plný text záznamu View this record from Arxiv