Existence and regularity of hypersurfaces with prescribed mean curvature and a free boundary.
Existence of minimizers for non-quasiconvex functionals arising in optimal design
Existence of solutions for the one-phase and the multi-layer free-boundary problems with the -Laplacian operator.
Fast level set based algorithms using shape and topological sensitivity information
First variation of the general curvature-dependent surface energy
We consider general surface energies, which are weighted integrals over a closed surface with a weight function depending on the position, the unit normal and the mean curvature of the surface. Energies of this form have applications in many areas, such as materials science, biology and image processing. Often one is interested in finding a surface that minimizes such an energy, which entails finding its first variation with respect to perturbations of the surface. We present a concise derivation...
First variation of the general curvature-dependent surface energy
We consider general surface energies, which are weighted integrals over a closed surface with a weight function depending on the position, the unit normal and the mean curvature of the surface. Energies of this form have applications in many areas, such as materials science, biology and image processing. Often one is interested in finding a surface that minimizes such an energy, which entails finding its first variation with respect to perturbations of the surface. We present a concise derivation...
Free Boundary Problem for capillary surfaces.
Global minimizer of the ground state for two phase conductors in low contrast regime
The problem of distributing two conducting materials with a prescribed volume ratio in a ball so as to minimize the first eigenvalue of an elliptic operator with Dirichlet conditions is considered in two and three dimensions. The gap ε between the two conductivities is assumed to be small (low contrast regime). The main result of the paper is to show, using asymptotic expansions with respect to ε and to small geometric perturbations of the optimal shape, that the global minimum of the first eigenvalue...
Global minimizers for axisymmetric multiphase membranes
We consider a Canham − Helfrich − type variational problem defined over closed surfaces enclosing a fixed volume and having fixed surface area. The problem models the shape of multiphase biomembranes. It consists of minimizing the sum of the Canham − Helfrich energy, in which the bending rigidities and spontaneous curvatures are now phase-dependent, and a line tension penalization for the phase interfaces. By restricting attention to axisymmetric surfaces and phase distributions, we extend our previous...
Global minimizing domains for the first eigenvalue of an elliptic operator with non-constant coefficients.
Global solution of optimal shape design problems.
Hadamard incomplete sensitivity and shape optimization
How to blow infinitely large soap bubbles with a fixed boundary
How to prove existence in shape optimization
Hybrid level set phase field method for topology optimization of contact problems
The paper deals with the analysis and the numerical solution of the topology optimization of system governed by variational inequalities using the combined level set and phase field rather than the standard level set approach. The standard level set method allows to evolve a given sharp interface but is not able to generate holes unless the topological derivative is used. The phase field method indicates the position of the interface in a blurry way but is flexible in the holes generation. In the...
Hybrid variational formulation of an elliptic state equation applied to an optimal shape problem
Incompressible Maxwell-Boussinesq approximation: Existence, uniqueness and shape sensitivity
Inégalité isopérimétrique en dimension 3 d'après B. Kleiner
Influence of a boundary perforation on the Dirichlet energy
Inverse modelling of image-based patient-specific blood vessels: zero-pressure geometry and in vivo stress incorporation
In vivo visualization of cardiovascular structures is possible using medical images. However, one has to realize that the resulting 3D geometries correspond to in vivo conditions. This entails an internal stress state to be present in the in vivo measured geometry of e.g. a blood vessel due to the presence of the blood pressure. In order to correct for this in vivo stress, this paper presents an inverse method to restore the original zero-pressure geometry of a structure, and to recover the in vivo...