We consider the following problem, arising within a geological model of sedimentationerosion: For a given vector field g and a given nonnegative function F defined on a oneor twodimensional domain Ω, find a vector field under the form g̃ = ug, with 0 ≤ u(x) ≤ 1 for a.e. x ∈ Ω, such that divg̃ + F ≥ 0 and (u − 1)(divg̃ + F ) = 0 in Ω. We first give a weak formulation of this problem, and we prove a...

Given a Gibbs point process P on R having a weak enough potential Ψ, we consider the random measures μλ := P x∈P∩Qλ ξ(x,P ∩Qλ)δx/λ1/d , where Qλ := [−λ /2, λ/2] is the volume λ cube and where ξ(·, ·) is a translation invariant stabilizing functional. Subject to Ψ satisfying a localization property and translation invariance, we establish weak laws of large numbers for λ−1μλ(f), f a bounded test...

Abstract In this article, we provide necessary and sufficient conditions for the existence of non-norm-attaining operators in $\mathcal {L}(E, F)$ . By using a theorem due to Pfitzner on James boundaries, show that if there exists relatively compact set K (in weak operator topology) such $0$ is an element its closure but it not norm-closed convex hull, then can guarantee does attain norm. This ...

in this paper,  we introduce the notion of  generalized multivalued  $f$- weak contraction and we prove some fixed point theorems related to introduced  contraction for multivalued mapping in complete metric spaces.  our results extend and improve the results announced by many others with less hypothesis. also, we give some illustrative examples.

Let $f\colon Y \to X$ be a proper flat morphism of locally noetherian schemes. Then the locus in $X$ over which $f$ is smooth stable under generization. We prove that, suitable assumptions on formal fibers , same property holds for other local properties morphisms, even if only closed and flat. Our proof this statement reduces to purely question known as Grothendieck's localization problem. To ...

The (PS)-weak lower semicontinuity property has been introduced in Vasiliu and Yan [10] for general continuously differentiable functionals on Sobolev spaces in connection with the Ekeland variational principle and the direct method of calculus of variations. In this paper, we give a necessary and sufficient condition of this property for the functionals in one-dimension of the simple type I(u)...

Suppose that the consumption side of a constant returns production economy is described by an excess demand function f: R’,, -+ R’ satisfying the usual properties of continuity, homogeneity of degree zero, and p. f( p) = 0 for all p. A property of central importance is the Weak Axiom of Revealed Preference (WA). The excess demand function f satisfies WA iff(p)#f(q) and q.f(p)O....