Note sur l'impossibilité de la quadrature du cercle
Numerical finiteness results for minimal surfaces in three-dimensional space forms.
Numerical minimization of eigenmodes of a membrane with respect to the domain
In this paper we introduce a numerical approach adapted to the minimization of the eigenmodes of a membrane with respect to the domain. This method is based on the combination of the Level Set method of S. Osher and J.A. Sethian with the relaxed approach. This algorithm enables both changing the topology and working on a fixed regular grid.
Numerical minimization of eigenmodes of a membrane with respect to the domain
In this paper we introduce a numerical approach adapted to the minimization of the eigenmodes of a membrane with respect to the domain. This method is based on the combination of the Level Set method of S. Osher and J.A. Sethian with the relaxed approach. This algorithm enables both changing the topology and working on a fixed regular grid.
Numerical realization of a fictitious domain approach used in shape optimization. Part I: Distributed controls
We deal with practical aspects of an approach to the numerical realization of optimal shape design problems, which is based on a combination of the fictitious domain method with the optimal control approach. Introducing a new control variable in the right-hand side of the state problem, the original problem is transformed into a new one, where all the calculations are performed on a fixed domain. Some model examples are presented.
Numerical simulations for nodal domains and spectral minimal partitions
We recall here some theoretical results of Helffer et al. [Ann. Inst. H. Poincaré Anal. Non Linéaire (2007) doi:10.1016/j.anihpc.2007.07.004] about minimal partitions and propose numerical computations to check some of their published or unpublished conjectures and exhibit new ones.
Numerical solution of soap film dual problems.
Numerical solution of the pressing devices shape optimization problem in the glass industry
In this contribution, we present the problem of shape optimization of the plunger cooling which comes from the forming process in the glass industry. We look for a shape of the inner surface of the insulation barrier located in the plunger cavity so as to achieve a constant predetermined temperature on the outward surface of the plunger. A rotationally symmetric system, composed of the mould, the glass piece, the plunger, the insulation barrier and the plunger cavity, is considered. The state problem...
Numerical study of a new global minimizer for the Mumford-Shah functional in R3
In [Progress Math.233 (2005)], David suggested the existence of a new type of global minimizers for the Mumford-Shah functional in . The singular set of such a new minimizer belongs to a three parameters family of sets . We first derive necessary conditions satisfied by global minimizers of this family. Then we are led to study the first eigenvectors of the Laplace-Beltrami operator with Neumann boundary conditions on subdomains of with three reentrant corners. The necessary conditions are...
O 19. a 20. Hilbertově problému
Of the structure of the Euler mapping
On a class of variational integrals over BV varieties
We present here our most recent results ([1def]) about the definition of non-linear Weiertrass-type integrals over BV varieties, possibly discontinuous and not necessarily Sobolev's.
On a class of variational problems defined by polynomial Lagrangians
On a conjecture by Auerbach
In 1938 Herman Auerbach published a paper where he showed a deep connection between the solutions of the Ulam problem of floating bodies and a class of sets studied by Zindler, which are the planar sets whose bisecting chords all have the same length. In the same paper he conjectured that among Zindler sets the one with minimal area, as well as with maximal perimeter, is the so-called “Auerbach triangle”. We prove this conjecture.
On a critical point theory for minimal surfaces spanning a wire in Rn.
On a functional depending on curvature and edges
On a general coarea inequality and applications.
On a magnetic characterization of spectral minimal partitions
Given a bounded open set in (or in a Riemannian manifold) and a partition of by open sets , we consider the quantity where is the ground state energy of the Dirichlet realization of the Laplacian in . If we denote by the infimum over all the -partitions of , a minimal -partition is then a partition which realizes the infimum. When , we find the two nodal domains of a second eigenfunction, but the analysis of higher ’s is non trivial and quite interesting. In this paper, we give...
On a problem of Monge.
On a system of partial differential equations in Heisenberg space. (Sur un système d'équations aux d'érivées partielles dans l'espace de Heisenberg.)