On the minimal displacement of points under mappings
New contributions concerning the minimal displacement of points under mappings (defect of fixed point) are obtained.
On the minimization of some nonconvex double obstacle problems.
On the minimizers of the Möbius cross energy of links.
On the minimum of the work of interaction forces between a pseudoplate and a rigid obstacle
An optimization problem for the unilateral contact between a pseudoplate and a rigid obstacle is considered. The variable thickness of the pseudoplate plays the role of a control variable. The cost functional is a regular functional only in the smooth case. The existence of an optimal thickness is verified. The penalized optimal control problem is considered in the general case.
On the minimum time control problem and continuous families of convex sets
On the minimum time problem in linear discrete systems with the discrete set of admissible controls
On the Morse Index of Minmal Surfaces in IRp with Polygonal Boundaries.
On the necessary condition for the optimality of control in the problem of evasion in differential games
On the Newton partially flat minimal resistance body type problems
We study the flat region of stationary points of the functional under the constraint , where is a bounded domain in . Here is a function which is concave for small and convex for large, and is a given constant. The problem generalizes the classical minimal resistance body problems considered by Newton. We construct a family of partially flat radial solutions to the associated stationary problem when is a ball. We also analyze some other qualitative properties. Moreover, we show the...
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 nonlinear elastic simply supported beam equation.
On the nonlinear implicit complementarity problem.
On the non-locality of quasiconvexity
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 notion of Jacobi fields in constrained calculus of variations
In variational calculus, the minimality of a given functional under arbitrary deformations with fixed end-points is established through an analysis of the so called second variation. In this paper, the argument is examined in the context of constrained variational calculus, assuming piecewise differentiable extremals, commonly referred to as extremaloids. The approach relies on the existence of a fully covariant representation of the second variation of the action functional, based on a family of...
On the numerical approximation of first-order Hamilton-Jacobi equations
Some methods for the numerical approximation of time-dependent and steady first-order Hamilton-Jacobi equations are reviewed. Most of the discussion focuses on conformal triangular-type meshes, but we show how to extend this to the most general meshes. We review some first-order monotone schemes and also high-order ones specially dedicated to steady problems.
On the numerical modeling of deformations of pressurized martensitic thin films
We propose, analyze, and compare several numerical methods for the computation of the deformation of a pressurized martensitic thin film. Numerical results have been obtained for the hysteresis of the deformation as the film transforms reversibly from austenite to martensite.
On the Numerical Modeling of Deformations of Pressurized Martensitic Thin Films
We propose, analyze, and compare several numerical methods for the computation of the deformation of a pressurized martensitic thin film. Numerical results have been obtained for the hysteresis of the deformation as the film transforms reversibly from austenite to martensite.
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.