On the equivalence of variational problems. III
On the ersatz material approximation in level-set methods
The level set method has become widely used in shape optimization where it allows a popular implementation of the steepest descent method. Once coupled with a ersatz material approximation [Allaire et al., J. Comput. Phys.194 (2004) 363–393], a single mesh is only used leading to very efficient and cheap numerical schemes in optimization of structures. However, it has some limitations and cannot be applied in every situation. This work aims at exploring such a limitation. We estimate the systematic...
On the evaluation of finite element sensitivities to nodal coordinates.
On the existence of area-minimizing surfaces with free boundary.
On the Existence of Integral Currents with Prescribed Mean Curvature Vector.
On the Existence of Surfaces with Prescribed Mean Curvature and Boundary.
On the existence of surfaces with prescribed mean curvature and boundary in higher dimensions
On the extremals of a subsidiary capillary problem.
On the Global Structure of Crystalline Surfaces.
On the hessian of the optimal transport potential
We study the optimal solution of the Monge-Kantorovich mass transport problem between measures whose density functions are convolution with a gaussian measure and a log-concave perturbation of a different gaussian measure. Under certain conditions we prove bounds for the Hessian of the optimal transport potential. This extends and generalises a result of Caffarelli. We also show how this result fits into the scheme of Barthe to prove Brascamp-Lieb inequalities and thus prove a new generalised Reverse...
On the homogeneity of global minimizers for the Mumford-Shah functional when K is a smooth cone
On the isoperimetric inequality for minimal surfaces
On the Linear Isoperimetric Inequality.
On the minima of functionals with linear growth
On the Morse Index of Minmal Surfaces in IRp with Polygonal Boundaries.
On the Nonexistence of a Hypersurface of Prescribed Mean Curvature with a Given Boundary.
On the non-existence of energy stable minimal cones
On the normal variations of a domain
In domain optimization problems, normal variations of a reference domain are frequently used. We prove that such variations do not preserve the regularity of the domain. More precisely, we give a bounded domain which boundary is m times differentiable and a scalar variation which is infinitely differentiable such that the deformed boundary is only m-1 times differentiable. We prove in addition that the only normal variations which preserve the regularity are those with constant magnitude. This...
On the numerical solution of axisymmetric domain optimization problems
An axisymmetric second order elliptic problem with mixed boundarz conditions is considered. A part of the boundary has to be found so as to minimize one of four types of cost functionals. The numerical realization is presented in detail. The convergence of piecewise linear approximations is proved. Several numerical examples are given.
On the optimization of initial conditions for a model parameter estimation
The design of an experiment, e.g., the setting of initial conditions, strongly influences the accuracy of the process of determining model parameters from data. The key concept relies on the analysis of the sensitivity of the measured output with respect to the model parameters. Based on this approach we optimize an experimental design factor, the initial condition for an inverse problem of a model parameter estimation. Our approach, although case independent, is illustrated at the FRAP (Fluorescence...