5 citations · 14 across the 7 of their papers we have counts for
8 papers
Confined elastic wires of large length: the sharp second-order asymptotics
Luca Mugnai
We study the least bending energy of a closed embedded wire of prescribed length confined to the closed unit disk. It is classical that the bending energy of any closed c…
Global solutions to the volume-preserving mean-curvature flow
Luca Mugnai, Christian Seis, Emanuele Spadaro
In this paper, we construct global distributional solutions to the volume-preserving mean-curvature flow using a variant of the time-discrete gradient flow approach proposed indepe…
A phase field model for the optimization of the Willmore energy in the class of connected surfaces
Patrick W. Dondl, Luca Mugnai, Matthias Röger
We consider the problem of minimizing the Willmore energy connected surfaces with prescribed surface area which are confined to a finite container. To this end, we approximate the…
Gamma-convergence results for phase-field approximations of the 2D-Euler Elastica Functional
Luca Mugnai
We establish some new results about the -limit, with respect to the -topology, of two different (but related) phase-field approximations of the so-called Euler's Elastica B…
Confined elastic curves
Patrick W. Dondl, Luca Mugnai, Matthias Röger
We consider the problem of minimizing Euler's elastica energy for simple closed curves confined to the unit disk. We approximate a simple closed curve by the zero level set of a fu…
Approximation of the Helfrich's functional via Diffuse Interfaces
Giovanni Bellettini, Luca Mugnai
We give a rigorous proof of the approximability of the so-called Helfrich's functional via diffuse interfaces, under a constraint on the ratio between the bending rigidity and the…