3 citations · 5 across the 3 of their papers we have counts for
4 papers
Scale-critical curve diffusion flows
Tatsuya Miura, Glen Wheeler
We introduce and study a one-parameter family of curve diffusion flows with a scale-critical cubic curvature term for closed immersed planar curves. We first classify all closed st…
The free elastic flow for closed planar curves
Tatsuya Miura, Glen Wheeler
The free elastic flow is the -gradient flow for Euler's elastic energy, or equivalently the Willmore flow with translation invariant initial data. In contrast to elastic flows…
Uniqueness and minimality of Euler's elastica with monotone curvature
Tatsuya Miura, Glen Wheeler
For an old problem of Euler's elastica we prove the novel global property that every planar elastica with non-constant monotone curvature is uniquely minimal subject to the clamped…
A mixed finite element method for a sixth order elliptic problem
Jérôme Droniou, Muhammad Ilyas, Bishnu Lamichhane +1
We consider a saddle point formulation for a sixth order partial differential equation and its finite element approximation, for two sets of boundary conditions. We follow the Ciar…