In this work, we study concentration properties for vector valued maps. In particular, we describe inequalities which capture the exact dimensional behavior of Lipschitz maps with values in Rk. To this task, we study in particular a domination principle for projections which might be of independent interest. We further compare our conclusions to earlier results by Pinelis in the Gaussian case, ...

for vector-valued functions u on Lipschitz domains Q c R. The right side of (1) is the relaxation of the left, cf. [1]. Each infimum is over u G if(Q;R), lsupp Vu denotes the characteristic function of the support of Vu, and \Vu\ = E(<hi7cte*)The left side of (1) is a problem of optimal design: it minimizes Area(H \ S) + fQ \Vus\ 2 dx, among all sets S c O , where us solves the variational problem

Ω ∇u · v, where u is harmonic in the domain Ω ≡ {(x, t) ∈ Rn+1 : t > φ(x)}, with φ Lipschitz, and where v ∈ W loc is vector valued. He showed that the bilinear form (1.1) is bounded by the L2 norm of the square function plus the non-tangential maximal function of u, times the same expression for v. In the present note, we generalize Dahlberg’s Theorem to variable coefficient divergence form ell...

Nonnegative measure-valued solutions of the continuity equation are uniquely determined by their initial condition, if the characteristic ODE associated to the velocity field has a unique solution. In this paper we give a partial extension of this result to signed measurevalued solutions, under a quantitative two-sided Osgood condition on the velocity field. Our results extend those obtained fo...

This paper explores relationships between many-valued logic and fuzzy topology from the viewpoint of duality theory. We first show a fuzzy topological duality for the algebras of Lukasiewicz n-valued logic with truth constants, which generalizes Stone duality for Boolean algebras to the n-valued case via fuzzy topology. Then, based on this duality, we show a fuzzy topological duality for the al...

For an algebra A of complex-valued, continuous functions on a compact Hausdorff space (X, τ), it is standard practice to assume that A separates points in the sense that for each distinct pair x, y ∈ X, there exists an f ∈ A such that f(x) 6= f(y). If A does not separate points, it is known that there exists an algebra  on a compact Hausdorff space (X̂, τ̂) that does separate points such that th...

In this paper‎, ‎we introduce and study some new single-valued gap functions for non-differentiable semi-infinite multiobjective optimization problems with locally Lipschitz data‎. ‎Since one of the fundamental properties of gap function for optimization problems is its abilities in characterizing the solutions of the problem in question‎, ‎then the essential properties of the newly introduced ...

We propose a Newton method for solving smooth unconstrained vector optimization problems under partial orders induced by general closed convex pointed cones. The method extends the one proposed by Fliege, Graña Drummond and Svaiter for multicriteria, which in turn is an extension of the classical Newton method for scalar optimization. The steplength is chosen by means of an Armijo-like rule, gu...