On the lower semicontinuity of functionals involving Lebesgue or improper Riemann integrals in infinite horizon optimal control problems
On the lower semicontinuity of supremal functionals
In this paper we study the lower semicontinuity problem for a supremal functional of the form with respect to the strong convergence in , furnishing a comparison with the analogous theory developed by Serrin for integrals. A sort of Mazur’s lemma for gradients of uniformly converging sequences is proved.
On the Lower Semicontinuity of Supremal Functionals
In this paper we study the lower semicontinuity problem for a supremal functional of the form with respect to the strong convergence in L∞(Ω), furnishing a comparison with the analogous theory developed by Serrin for integrals. A sort of Mazur's lemma for gradients of uniformly converging sequences is proved.
On the lower semicontinuous quasiconvex envelope for unbounded integrands (I)
Motivated by the study of multidimensional control problems of Dieudonné-Rashevsky type, we raise the question how to understand to notion of quasiconvexity for a continuous function f with a convex body K instead of the whole space as the range of definition. In the present paper, we trace the consequences of an infinite extension of f outside K, and thus study quasiconvex functions which are allowed to take the value +∞. As an appropriate envelope, we introduce and investigate the lower semicontinuous...
On the Łojasiewicz exponent at infinity of real polynomials
Let f: ℝⁿ → ℝ be a nonconstant polynomial function. Using the information from the "curve of tangency" of f, we provide a method to determine the Łojasiewicz exponent at infinity of f. As a corollary, we give a computational criterion to decide if the Łojasiewicz exponent at infinity is finite or not. Then we obtain a formula to calculate the set of points at which the polynomial f is not proper. Moreover, a relation between the Łojasiewicz exponent at infinity of f and the problem of computing...
On the Mazur-Orlicz theorem
On the measurability of the conjugate and the subdifferential of a normal integrand.
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 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 nonlinear elastic simply supported beam equation.
On the nonlinear implicit complementarity problem.
On the non-locality of quasiconvexity
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 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 obstacle problem with a volume constraint.