The concentration-compactness principle in the calculus of variations. The locally compact case, part 2
The concentration-compactness principle in the calculus of variations. The limit case, Part II.
This paper is the second part of a work devoted to the study of variational problems (with constraints) in functional spaces defined on domains presenting some (local) form of invariance by a non-compact group of transformations like the dilations in RN. This contains for example the class of problems associated with the determination of extremal functions in inequalities like Sobolev inequalities, convolution or trace inequalities... We show how the concentration-compactness principle and method...
The concentration-compactness principle in the calculus of variations. The limit case, Part I.
After the study made in the locally compact case for variational problems with some translation invariance, we investigate here the variational problems (with constraints) for example in RN where the invariance of RN by the group of dilatations creates some possible loss of compactness. This is for example the case for all the problems associated with the determination of extremal functions in functional inequalities (like for example the Sobolev inequalities). We show here how the concentration-compactness...
The constructive approach on existence of time optimal controls of system governed by nonlinear equations on Banach spaces.
The existence theorem for one class of optimal problems in Banach space.
The linear-quadratic optimal control problem for delay differential equations
In questo lavoro si considera il problema del controllo ottimo per un'equazione lineare con ritardo in uno spazio di Hilbert, con costo quadratico. Si dimostra che il problema della sintesi si traduce in una equazione di Riccati in uno opportuno spazio prodotto e si prova che tale equazione ammette un’unica soluzione.
The minimal-norm problem and Pontriagin's maximum principle for Banach spaces, II
The operation of infimal convolution [Book]
The perturbed generalized proximal point algorithm
Théorème de minimax sans topologie ni convexité
Dans cete note, nous présentons un théorème de minimax (Théorème A) formulé seulement en langage de la théorie des ensembles. Ce résultat permet de déduire de façon immédiate (en utilisant un lemme de topologie générale) plusieurs théorèmes de minimax bien connus.
Time-optimal control of nonlinear parabolic systems with constrained derivative of control, existence theorem
Topology optimization of systems governed by variational inequalities
This paper deals with the formulation of the necessary optimality condition for a topology optimization problem of an elastic body in unilateral contact with a rigid foundation. In the contact problem of Tresca, a given friction is governed by an elliptic variational inequality of the second order. The optimization problem consists in finding such topology of the domain occupied by the body that the normal contact stress along the contact boundary of the body is minimized. The topological derivative...
Translation invariant spaces and asymptotic properties of variational equations.
Two-dimensional stable Lavrentiev phenomenon with and without boundary conditions