Properties of solutions to second order evolution control systems. II.
Proprietà della convessificazione
Proprietà fini delle funzioni con deformazione limitata ed applicazioni a problemi variazionali
Proto-derivatives of partial subgradient mappings.
Proto-differentiability of set-valued mappings and its applications in optimization
Proximal smoothness and the lower- property.
Prox-regularization and solution of ill-posed elliptic variational inequalities
In this paper new methods for solving elliptic variational inequalities with weakly coercive operators are considered. The use of the iterative prox-regularization coupled with a successive discretization of the variational inequality by means of a finite element method ensures well-posedness of the auxiliary problems and strong convergence of their approximate solutions to a solution of the original problem. In particular, regularization on the kernel of the differential operator and regularization...
-functions on quasimetric spaces and fixed points for multivalued maps.
Quantized distributed output regulation of multi-agent systems
Motivated by digital communication channel, we consider the distributed output regulation problem for linear multi-agent systems with quantized state measurements. Quantizers take finitely many values and have an adjustable "zoom" parameter. Quantized distributed output regulation concerns designing distributed feedback by employing quantized technique for multi-agent systems such that all agents can track an active leader, and/or distributed disturbance rejection. With the solvability conditions...
Quasi-convex functions and quasi-monotone operators.
Quasiconvex functions can be approximated by quasiconvex polynomials
Let W be a function from the real m×n-matrices to the real numbers. If W is quasiconvex in the sense of the calculus of variations, then we show that W can be approximated locally uniformly by quasiconvex polynomials.
Quasiconvex functions, and two elastic wells
Quasiconvex relaxation of multidimensional control problems with integrands f(t, ξ, v)
We prove a general relaxation theorem for multidimensional control problems of Dieudonné-Rashevsky type with nonconvex integrands f(t, ξ, v) in presence of a convex control restriction. The relaxed problem, wherein the integrand f has been replaced by its lower semicontinuous quasiconvex envelope with respect to the gradient variable, possesses the same finite minimal value as the original problem, and admits a global minimizer. As an application, we provide existence theorems for the image registration...
Quasiconvex relaxation of multidimensional control problems with integrands f(t, ξ, v)
We prove a general relaxation theorem for multidimensional control problems of Dieudonné-Rashevsky type with nonconvex integrands f(t, ξ, v) in presence of a convex control restriction. The relaxed problem, wherein the integrand f has been replaced by its lower semicontinuous quasiconvex envelope with respect to the gradient variable, possesses the same finite minimal value as the original problem, and admits a global minimizer. As an application, we provide existence theorems for the image registration...
Quasiconvexity at the boundary and concentration effects generated by gradients
We characterize generalized Young measures, the so-called DiPerna–Majda measures which are generated by sequences of gradients. In particular, we precisely describe these measures at the boundary of the domain in the case of the compactification of ℝm × n by the sphere. We show that this characterization is closely related to the notion of quasiconvexity at the boundary introduced by Ball and Marsden [J.M. Ball and J. Marsden, Arch. Ration. Mech. Anal. 86 (1984) 251–277]. As a consequence we get...
Quasi-invariant optimal control problems.
Quasilinear elliptic equations with discontinuous coefficients
We prove an existence result for equations of the form where the coefficients satisfy the usual ellipticity conditions and hypotheses weaker than the continuity with respect to the variable . Moreover, we give a counterexample which shows that the problem above may have no solution if the coefficients are supposed only Borel functions
Quasilinear Elliptic-Parabolic Differentail Equations.
Quasi-minima
Quasi-norm error bounds for the finite element approximation of some degenerate quasilinear elliptic equations and variational inequalities