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Abstract This paper presents a differential criterion of n dimensional geometrically convex functions, and gives some applications.
This article is concerned with the existence result of the unilateral problem associated to the equations of the type Au – div φ ( u ) = ƒ ∈ L 1 (Ω), where A is a Leray-Lions operator having a growth not necessarily of polynomial type and φ ∈ C 0 (ℝ, ℝ N ).
Abstract We prove that if a pair 〈 I , J 〉 of ccc, translation invariant σ -ideals on 2 ω has the Fubini Property, then I = J . This leads to a slightly improved exposition of a part of the Farah-Zapletal proof of an invariant version of their theorem which characterizes the measure and...
Abstract We discuss the weak form of the Ramberg/Osgood equations (also known as the Norton/Hoff model) for nonlinear elastic materials on a 3-dimensional domain and show that the stress tensor is Hölder continuous on an open subset whose complement is of Lebesgue-measure zero. We also give an...
Abstract In this paper, we construct γ -regular Cl n -minimal function systems in , the generalized Bergman space of Cl n -valued functions in the Sobolev space which are used in the best way to approximate null solutions of the in-homogeneous Dirac operator.
The solvability of the generalized weak vector implicit variational inequality problem, generalized strong vector implicit variational inequality problem and generalized vector variational inequality problem are proved by using a generalized Fan's KKM theorem. Our results extend and unify...
Abstract The present paper provides first and second-order characterizations of a radially lower semicontinuous strictly pseudoconvex function ƒ : X → ℝ defined on a convex set X in the real Euclidean space ℝ n in terms of the lower Dini-directional derivative. In particular we obtain...
Abstract We introduce “probabilistic” and “stochastic Hilbertian structures”. These seem to be a suitable context for developing a theory of “quantum Gaussian processes”. The Schauder system is utilised to give a Lévy-Ciesielski representation of quantum (bosonic) Brownian motion as...
Abstract We investigate a class of over-determined parabolic problems involving a non-constant boundary condition. The Weinstein's technique known for the elliptic problems is extended to the parabolic one by means of auxiliary functions and Green classical formula.
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