Zobrazeno 1 - 10
of 117
pro vyhledávání: '"Lussardi, Luca"'
A review on the classical Plateau problem is presented. Then, the state of the art about the Kirchhoff-Plateau problem is illustrated as well as some possible future directions of research.
Externí odkaz:
http://arxiv.org/abs/2410.06179
We study a particular type of Einstein warped-product manifold where the warping function must satisfy the homogeneous version of the screened Poisson equation. Under these assumptions, we show that the dimension of the manifold, the (constant negati
Externí odkaz:
http://arxiv.org/abs/2407.20381
Nematic surfaces are thin fluid structures, ideally two-dimensional, endowed with an in-plane nematic order. In 2012, two variational models have been introduced by Giomi [10] and by Napoli and Vergori [27,26]. Both penalize the area of the surface a
Externí odkaz:
http://arxiv.org/abs/2405.20154
In this work, we demonstrate that a functional modeling the self-aggregation of stochastically distributed lipid molecules can be obtained as the $\Gamma$-limit of a family of discrete energies driven by a sequence of independent and identically dist
Externí odkaz:
http://arxiv.org/abs/2305.05761
We compare the Serret-Frenet frame with a {\em relatively parallel adapted frame} (RPAF) introduced by Bishop to parametrize $W^{2,2}$-curves. Next, we derive the geometric invariants, curvature and torsion, with the RPAF associated to the curve. Fin
Externí odkaz:
http://arxiv.org/abs/2301.03525
Publikováno v:
Z Angew Math Mech. e202300890 (2024)
We perform a variational analysis of an elastic membrane spanning a closed curve which may sustain bending and torsion. First, we deal with parametrized curves and linear elastic membranes proving the existence of equilibria and finding first-order n
Externí odkaz:
http://arxiv.org/abs/2207.13614
The existence of minimizers of the Canham--Helfrich functional in the setting of generalized Gauss graphs is proved. As a first step, the Canham--Helfrich functional, usually defined on regular surfaces, is extended to generalized Gauss graphs, then
Externí odkaz:
http://arxiv.org/abs/2201.06353
We minimize elastic energies on framed curves which penalize both curvature and torsion. We also discuss critical points using the infinite dimensional version of the Lagrange multipliers' method. Finally, some examples arising from the applications
Externí odkaz:
http://arxiv.org/abs/2106.01659
We consider the functional $\int_\Omega g(\nabla u+\textbf X^\ast)d\mathscr L^{2n}$ where $g$ is convex and $\textbf X^\ast(x,y)=2(-y,x)$ and we study the minimizers in $BV(\Omega)$ of the associated Dirichlet problem. We prove that, under the bounde
Externí odkaz:
http://arxiv.org/abs/2010.00782
We study the asymptotic behavior of a family of functionals which penalize a short-range interaction of convolution type between a finite perimeter set and its complement. We first compute the pointwise limit and we obtain a lower estimate on more re
Externí odkaz:
http://arxiv.org/abs/2008.13110