5 papers · 1 filter
Obstacle problems for the elastic flow and related topics
Kensuke Yoshizawa
In this note, we study an obstacle problem for the elastic flow. We prove the local-in-time existence of weak solutions and discuss their relation to classical solutions when addit…
Stability of flat-core pinned p-elasticae
Tatsuya Miura, Kensuke Yoshizawa
We classify the stability of flat-core -elasticae in subject to the pinned boundary condition. Together with previous work, this completes the classification of s…
A nongraphical obstacle problem for elastic curves
Marius Müller, Kensuke Yoshizawa
We study an obstacle problem for the length-penalized elastic bending energy for open planar curves pinned at the boundary. We first consider the case without length penalization a…
Classification and stability of penalized pinned elasticae
Marius Müller, Kensuke Yoshizawa
This paper considers critical points of the length-penalized elastic bending energy among planar curves whose endpoints are fixed. We classify all critical points with an explicit…
Variational stabilization of degenerate p-elasticae
Tatsuya Miura, Kensuke Yoshizawa
A new stabilization phenomenon induced by degenerate diffusion is discovered in the context of pinned planar -elasticae. It was known that in the non-degenerate regime $p\in(1,2…