A selection theory for multiple-valued functions in the sense of Almgren.
A self-adaptive method for solving a system of nonlinear variational inequalities.
A semi-smooth Newton method for solving elliptic equations with gradient constraints
Semi-smooth Newton methods for elliptic equations with gradient constraints are investigated. The one- and multi-dimensional cases are treated separately. Numerical examples illustrate the approach and as well as structural features of the solution.
A semi-smooth Newton method for solving elliptic equations with gradient constraints
Semi-smooth Newton methods for elliptic equations with gradient constraints are investigated. The one- and multi-dimensional cases are treated separately. Numerical examples illustrate the approach and as well as structural features of the solution.
A set oriented approach to global optimal control
We describe an algorithm for computing the value function for “all source, single destination” discrete-time nonlinear optimal control problems together with approximations of associated globally optimal control strategies. The method is based on a set oriented approach for the discretization of the problem in combination with graph-theoretic techniques. The central idea is that a discretization of phase space of the given problem leads to an (all source, single destination) shortest path problem...
A set oriented approach to global optimal control
We describe an algorithm for computing the value function for “all source, single destination” discrete-time nonlinear optimal control problems together with approximations of associated globally optimal control strategies. The method is based on a set oriented approach for the discretization of the problem in combination with graph-theoretic techniques. The central idea is that a discretization of phase space of the given problem leads to an (all source, single destination) shortest path...
A shape-optimization technique for the capillary surface problem.
A simple proof of the minimax-theorem
A simple proof of the Rademacher theorem
A stochastic impulse control problem with quadratic growth Hamiltonian and the corresponding quasi variational inequality.
A strongly nonlinear problem arising in glaciology
The computation of glacier movements leads to a system of nonlinear partial differential equations. The existence and uniqueness of a weak solution is established by using the calculus of variations. A discretization by the finite element method is done. The solution of the discrete problem is proved to be convergent to the exact solution. A first simple numerical algorithm is proposed and its convergence numerically studied.
A study of a unilateral and adhesive contact problem with normal compliance
The aim of this paper is to study a quasistatic unilateral contact problem between an elastic body and a foundation. The constitutive law is nonlinear and the contact is modelled with a normal compliance condition associated to a unilateral constraint and Coulomb's friction law. The adhesion between contact surfaces is taken into account and is modelled with a surface variable, the bonding field, whose evolution is described by a first-order differential equation. We establish a variational formulation...
A study of variational inequalities for set-valued mappings.
A superquadratic method for solving variational inclusions under weak conditions.
A topological asymptotic analysis for the regularized grey-level image classification problem
The aim of this article is to propose a new method for the grey-level image classification problem. We first present the classical variational approach without and with a regularization term in order to smooth the contours of the classified image. Then we present the general topological asymptotic analysis, and we finally introduce its application to the grey-level image classification problem.
A unified optimality condition for eigenvalue problems
A unilateral boundary-value problem for the rod
A unilateral boundary-value condition at the left end of a simply supported rod is considered. Variational and (equivalent) classical formulations are introduced and all solutions to the classical problem are calculated in an explicit form. Formulas for the energies corresponding to the solutions are also given. The problem is solved and energies of the solutions are compared in the pertubed as well as the unperturbed cases.
A unilateral contact problem with slip-dependent friction
We consider a mathematical model which describes a static contact between a nonlinear elastic body and an obstacle. The contact is modelled with Signorini's conditions, associated with a slip-dependent version of Coulomb's nonlocal friction law. We derive a variational formulation and prove its unique weak solvability. We also study the finite element approximation of the problem and obtain an optimal error estimate under extra regularity for the solution. Finally, we establish the convergence of...
A variant of Newton's method for generalized equations.
A variational approach to implicit ODEs and differential inclusions
An alternative approach for the analysis and the numerical approximation of ODEs, using a variational framework, is presented. It is based on the natural and elementary idea of minimizing the residual of the differential equation measured in a usual Lp norm. Typical existence results for Cauchy problems can thus be recovered, and finer sets of assumptions for existence are made explicit. We treat, in particular, the cases of an explicit ODE and a differential inclusion. This approach also allows...