This article is devoted to analyze control properties for the heat equation with singular potential −μ/|x| arising at the boundary of a smooth domain Ω ⊂ R , N ≥ 1. This problem was firstly studied by Vancostenoble and Zuazua [18] and then generalized by Ervedoza [8] in the context of interior singularity. Roughly speaking, these results showed that for any value of parameters μ ≤ μ(N) := (N − ...

By virtue of convexification techniques, we study best approximations to a closed set C in a Hilbert space as well as perturbation conditions relative to C and a nonlinear inequality system. Some results on equivalence of the best approximation and the basic constraint qualification are established.

This paper concerns second order sufficient conditions of optimality, involving the Riccati equation, for optimal control problems with periodic boundary conditions. The problems considered involve no pathwise constraints and are ‘regular’, in the sense that the strengthened Legendre-Clebsch condition is assumed to be satisfied. A well-known sufficient condition, which we refer to as the Riccat...

and Applied Analysis 3 and in H1 Ω , respectively, observe that H⊥, the orthogonal complement of H in L2 Ω , is {∇p : p ∈ H1 Ω } cf. 11 or 12 . ii We denote P : L2 Ω 3 → H the L2 orthogonal projection, usually referred as Helmholtz-Leray projector, and by A −PΔ the Stokes operator with domain D A H2 Ω 3 ∩ V . Notice that in the case of periodic boundary condition, A −Δ|D A is a selfadjoint posi...

In this article we examine the behavior of optimal design models when the parameters are progressively unfixed in a process referred to as design aggregation. While this is a common modeling practice, its consequences on solution properties are not always predictable. Using no special assumptions on problem data, we develop an upper bound result for the aggregation process and highlight the dif...

This paper concerns applications of advanced techniques of variational analysis and generalized differentiation to problems of semi-infinite and infinite programming with feasible solution sets defined by parameterized systems of infinitely many linear inequalities of the type intensively studied in the preceding development [5) from our viewpoint of robust Lipschitzian stability. We present me...

A nonrandom sample of North American cases of sudden mass assault by a single individual (SMASI, n = 30) is compared with a nonrandom sample of Laotian amok cases (n = 18) and other amok studies. Perpetrators in both studies show evidence of social isolation, loss, depression, anger, pathological narcissism, and paranoia, often to a psychotic degree. The term "innovative perpetrator" is reintro...

There are a number of factors that influence compliance with prescribed plans of care. However, there remains a need to identify the collective source health, behavioral, and social constructs have on treatment satisfaction. This study aimed to identify indicators of pain treatment satisfaction among older adults receiving outpatient treatment from a comprehensive cancer center in the southeast...

There are a number of factors that influence compliance with prescribed plans of care. However, there remains a need to identify the collective source health, behavioral, and social constructs have on treatment satisfaction. This study aimed to identify indicators of pain treatment satisfaction among older adults receiving outpatient treatment from a comprehensive cancer center in the southeast...

Variational inequalities over sets defined by systems of equalities and inequalities are considered. A new reformulation of the KKT-conditions of the variational inequality as a system of equations is proposed. A related unconstrained minimization reformulation is also investigated. As a by-product of the analysis, a new characterization of strong regularity of KKT-points is given.