Remarks on the Regularity of Weak Solutions to Some Variational Inequalities.
Remarks on the theory of elasticity
In compressible Neohookean elasticity one minimizes functionals which are composed by the sum of the norm of the deformation gradient and a nonlinear function of the determinant of the gradient. Non–interpenetrability of matter is then represented by additional invertibility conditions. An existence theory which includes a precise notion of invertibility and allows for cavitation was formulated by Müller and Spector in 1995. It applies, however, only if some -norm of the gradient with is controlled...
Remarks on -quasiconvexity, interpenetration of matter, and function spaces for elasticity
Remarks on -stability of the conformal set in higher dimensions
Removable singularities for bounded -harmonic functions and quasi(super)harmonic functions.
Removing holes in topological shape optimization
The gradient based topological optimization tools introduced during the last ten years tend naturally to modify the topology of a domain by creating small holes inside the domain. Once these holes have been created, they usually remain unchanged, at least during the topological phase of the optimization algorithm. In this paper, a new asymptotic expansion is introduced which allows to decide whether an existing hole must be removed or not for improving the cost function. Then, two numerical examples...
Removing holes in topological shape optimization
The gradient based topological optimization tools introduced during the last ten years tend naturally to modify the topology of a domain by creating small holes inside the domain. Once these holes have been created, they usually remain unchanged, at least during the topological phase of the optimization algorithm. In this paper, a new asymptotic expansion is introduced which allows to decide whether an existing hole must be removed or not for improving the cost function. Then, two numerical...
Répartition optimale de la puissance dans une centrale hydraulique à réserve pompée
Representation formulas for L∞ norms of weakly convergent sequences of gradient fields in homogenization
We examine the composition of the L∞ norm with weakly convergent sequences of gradient fields associated with the homogenization of second order divergence form partial differential equations with measurable coefficients. Here the sequences of coefficients are chosen to model heterogeneous media and are piecewise constant and highly oscillatory. We identify local representation formulas that in the fine phase limit provide upper bounds on the limit superior of the L∞ norms of gradient fields. The...
Representation formulas for L∞ norms of weakly convergent sequences of gradient fields in homogenization
We examine the composition of the L∞ norm with weakly convergent sequences of gradient fields associated with the homogenization of second order divergence form partial differential equations with measurable coefficients. Here the sequences of coefficients are chosen to model heterogeneous media and are piecewise constant and highly oscillatory. We identify local representation formulas that in the fine phase limit provide upper bounds on the limit...
Resilient asynchronous primal Schur method
This paper introduces the application of asynchronous iterations theory within the framework of the primal Schur domain decomposition method. A suitable relaxation scheme is designed, whose asynchronous convergence is established under classical spectral radius conditions. For the usual case where local Schur complement matrices are not constructed, suitable splittings based only on explicitly generated matrices are provided. Numerical experiments are conducted on a supercomputer for both Poisson's...
Résolution d'un programme quadratique en variantes bivalentes par décomposition application au placement de commutateurs dans un réseau
Résolution numérique de certains problèmes de commande optimale
Resolvent iterative methods for solving system of extended general variational inclusions.
Resolvents and selections of accretive mappings in Banach spaces
Resonance of minimizers for n-level quantum systems with an arbitrary cost
We consider an optimal control problem describing a laser-induced population transfer on a -level quantum system. For a convex cost depending only on the moduli of controls (i.e. the lasers intensities), we prove that there always exists a minimizer in resonance. This permits to justify some strategies used in experimental physics. It is also quite important because it permits to reduce remarkably the complexity of the problem (and extend some of our previous results for and ): instead of looking...
Resonance of minimizers for n-level quantum systems with an arbitrary cost
We consider an optimal control problem describing a laser-induced population transfer on a n-level quantum system. For a convex cost depending only on the moduli of controls (i.e. the lasers intensities), we prove that there always exists a minimizer in resonance. This permits to justify some strategies used in experimental physics. It is also quite important because it permits to reduce remarkably the complexity of the problem (and extend some of our previous results for n=2 and n=3): instead...
Restrictive metric regularity and generalized differential calculus in Banach spaces.
Results for an optimal control problem with a semilinear state equation with constrained control
Results on existence of solution for an optimal design problem.
In this paper we study a control problem for elliptic nonlinear monotone problems with Dirichlet boundary conditions where the control variables are the coefficients of the equation and the open set where the partial differential problem is studied.