4 citations · 12 across the 11 of their papers we have counts for
11 papers
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…
General rigidity principles for stable and minimal elastic curves
Tatsuya Miura, Kensuke Yoshizawa
For a wide class of curvature energy functionals defined for planar curves under the fixed-length constraint, we obtain optimal necessary conditions for global and local minimizers…
Pinned planar p-elasticae
Tatsuya Miura, Kensuke Yoshizawa
Building on our previous work, we classify all planar -elasticae under the pinned boundary condition, and then obtain uniqueness and geometric properties of global minimizers. A…
A remark on elastic graphs with the symmetric cone obstacle
Kensuke Yoshizawa
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 satisfi…
Complete classification of planar p-elasticae
Tatsuya Miura, Kensuke Yoshizawa
Euler's elastica is defined by a critical point of the total squared curvature under the fixed length constraint, and its -counterpart is called -elastica. In this paper we…
An obstacle problem for the p-elastic energy
Anna Dall'Acqua, Marius Müller, Shinya Okabe +1
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 equa…
The critical points of the elastic energy among curves pinned at endpoints
Kensuke Yoshizawa
In this paper we find curves minimizing the elastic energy among curves whose length is fixed and whose ends are pinned. Applying the shooting method, we can identify all critical…