An approach of deterministic control problems with unbounded data
An approximation method in stochastic optimization and control
An approximation of solutions of variational inequalities.
An approximation scheme for the optimal control of diffusion processes
An approximation theorem for sequences of linear strains and its applications
We establish an approximation theorem for a sequence of linear elastic strains approaching a compact set in by the sequence of linear strains of mapping bounded in Sobolev space . We apply this result to establish equalities for semiconvex envelopes for functions defined on linear strains via a construction of quasiconvex functions with linear growth.
An approximation theorem for sequences of linear strains and its applications
We establish an approximation theorem for a sequence of linear elastic strains approaching a compact set in L1 by the sequence of linear strains of mapping bounded in Sobolev space W1,p . We apply this result to establish equalities for semiconvex envelopes for functions defined on linear strains via a construction of quasiconvex functions with linear growth.
An approximation to discrete optimal feedback controls.
An approximative method for solving the non-linear optimal control problem
An asymptotic condition for variational points of nonquadratic functionals
An asymptotical variational principle associated with the steepest descent method for a convex function.
An autonomous vehicle sequencing problem at intersections: A genetic algorithm approach
This paper addresses a vehicle sequencing problem for adjacent intersections under the framework of Autonomous Intersection Management (AIM). In the context of AIM, autonomous vehicles are considered to be independent individuals and the traffic control aims at deciding on an efficient vehicle passing sequence. Since there are considerable vehicle passing combinations, how to find an efficient vehicle passing sequence in a short time becomes a big challenge, especially for more than one intersection....
An elementary proof of Marcellini Sbordone semicontinuity theorem
The weak lower semicontinuity of the functional is a classical topic that was studied thoroughly. It was shown that if the function is continuous and convex in the last variable, the functional is sequentially weakly lower semicontinuous on . However, the known proofs use advanced instruments of real and functional analysis. Our aim here is to present a proof understandable even for students familiar only with the elementary measure theory.
An Elliptic Neumann Problem with Subcritical Nonlinearity
We establish the existence of a solution to the Neumann problem in the half-space with a subcritical nonlinearity on the boundary. Solutions are obtained through the constrained minimization or minimax. The existence of solutions depends on the shape of a boundary coefficient.
An Embedding Theorem in the Calculus of Variations for Multiple Integrals.
An estimation of the controllability time for single-input systems on compact Lie Groups
Geometric control theory and Riemannian techniques are used to describe the reachable set at time t of left invariant single-input control systems on semi-simple compact Lie groups and to estimate the minimal time needed to reach any point from identity. This method provides an effective way to give an upper and a lower bound for the minimal time needed to transfer a controlled quantum system with a drift from a given initial position to a given final position. The bounds include diameters...
An evolutionary double-well problem
An example in the gradient theory of phase transitions
We prove by giving an example that when the asymptotic behavior of functionals is quite different with respect to the planar case. In particular we show that the one-dimensional ansatz due to Aviles and Giga in the planar case (see [2]) is no longer true in higher dimensions.
An example in the gradient theory of phase transitions
We prove by giving an example that when n ≥ 3 the asymptotic behavior of functionals is quite different with respect to the planar case. In particular we show that the one-dimensional ansatz due to Aviles and Giga in the planar case (see [2]) is no longer true in higher dimensions.
An example of non-convex minimization and an application to Newton's problem of the body of least resistance
An existence and uniqueness result for Hamilton-Jacobi equations in Hilbert spaces
We prove an existence and uniqueness result for a class of Hamilton-Jacobi equations in Hilbert spaces.