12 documents found, page 1 of 2
Análise Multívoca e não Suave
Goncharov, VladimirTrata-se de uma publicação póstuma de um livro que estava a ser preparado para as provas de agregação do autor. É um livro que abrange várias áreas da Análise Multívoca e da Análise não Suave, onde todos os resultados são demonstrados, sendo algumas demonstrações originais, e com vários exemplos ilustrativos. É um texto para especialistas, investigadores e estudantes de Matemática e suas Aplicações.
Análise Multívoca e não Suave
Goncharov, VladimirTrata-se de uma publicação póstuma de um livro que estava a ser preparado para as provas de agregação do autor. É um livro que abrange várias áreas da Análise Multívoca e da Análise não Suave, onde todos os resultados são demonstrados, sendo algumas demonstrações originais, e com vários exemplos ilustrativos. É um texto para especialistas, investigadores e estudantes de Matemática e suas Aplicações.
Vector variational problem with knitting boundary conditions
Carita, Graça; Goncharov, Vladimir; Smirnov, GeorgiWe consider a variational problem with a polyconvex integrand and nonstandard boundary conditions that can be treated as minimization of the strain energy during the suturing process in plastic surgery. Existence of minimizers is proved and necessary optimality conditions are discussed.
Geometric conditions for regularity of viscosity solution to the simplest Hamil...
Goncharov, Vladimir; Pereira, FátimaContinuing research <cite>GP1, GP2</cite> on the well-posedness of the time-minimum problem with a constant convex dynamics (in a Hilbert space), we adapt one of the regularity conditions obtained there to a slightly more general problem, where nonaffine additive term appears. We prove existence and uniqueness of a minimizer in this problem as well as continuous differentiability of the value function (it can b...
An extremal property of the inf- and sup-convolutions regarding the Strong Maxi...
Goncharov, Vladimir; Santos, TelmaIn this paper we continue investigations started in [6] concerning the extension of the variational Strong Maximum Principle for lagrangeans depending on the gradient through a Minkowski gauge. We essentially enlarge the class of comparison functions, which substitute the identical zero when the lagrangean is not longer strictly convex at the origin
Brownian motion and exposed solutions of differential inclusions
Colombo, Giovanni; Goncharov, VladimirWe present a research program designed by A. Bressan and some partial results related to it. First, we construct a probability measure supported on the space of solutions to a planar differential inclusion, where the right hand side is a Lipschitz continuous segment. Such measure assigns probability one to solutions having derivatives a.e. equal to one of the endpoints of the segment. Second, for a class of pla...
Geometric conditions for regularity in a time-minimum problem with constant dyn...
Goncharov, Vladimir; Pereira, FátimaContinuing the earlier research on local well-posedness of a time-minimum problem associated to a closed target set C in a Hilbert space H and a convex constant dynamics F we study the Lipschitz (or, in general, Hölder) regularity of the (unique) point in C achieved from x for a minimal time. As a consequence, smoothness of the value function is proved, and an explicit formula for its derivative is given.
Local estimates for minimizers of some convex integral functional of the gradie...
Goncharov, Vladimir; Santos, TelmaWe consider a class of convex integral functionals with lagrangeans depending only on the gradient and satisfying a generalized symmetry assumption, which includes as a particular case the rotational symmetry. Adapting the method by A. Cellina we obtain a kind of local estimates for minimizers in the respective variational problems, which is applied then to deduce some versions of the Strong Maximum Principle i...
Well-posedness of minimal time problems with constant dynamics in Banach spaces
Colombo, Giovanni; Goncharov, Vladimir; Mordukhovich, BorisThis paper concerns the study of a general minimal time problem with a convex constant dynamics and a closed target set in Banach spaces. We pay the main attention to deriving sufficient conditions for the major well-posedness properties that include the existence and uniqueness of optimal solutions as well as certain regularity of the optimal value function with respect to state variables. Most of the results ...
Neighbourhood retractions of nonconvex sets in a Hilbert space via sublinear fu...
Goncharov, Vladimir; Pereira, FatimaFor a closed subset C of a Hilbert space and for a sublinear functional, which is equivalent to the norm, we give conditions guaranteeing existence and uniqueness of the nearest points to C in the sense of the semidistance generated by given sublinear functional. This permits us to construct a continuous retraction onto C well defined in an open neighbourhood of C. In particular, according to one of the conditi...