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New variants of Khintchine's inequality.

Ioan Serb (2001)

Collectanea Mathematica

Variants of Khintchine's inequality with coefficients depending on the vector dimension are proved. Equality is attained for different types of extremal vectors. The Schur convexity of certain attached functions and direct estimates in terms of the Haagerup type of functions are also used.

Non-compact lamination convex hulls

Jan Kolář (2003)

Annales de l'I.H.P. Analyse non linéaire

Nonconvex Lipschitz function in plane which is locally convex outside a discontinuum

Dušan Pokorný (2014)

Commentationes Mathematicae Universitatis Carolinae

We construct a Lipschitz function on $ℝ^{2}$ which is locally convex on the complement of some totally disconnected compact set but not convex. Existence of such function disproves a theorem that appeared in a paper by L. Pasqualini and was also cited by other authors.

Non-parametric convex hypersurfaces with a curvature restriction

Rolf Schneider (1983)

Annales Polonici Mathematici

Note On H-Convex Functions

Rade Živaljević (1979)

Publications de l'Institut Mathématique

Note on H-convex functions.

R. Zivaljevic (1979)

Publications de l'Institut Mathématique [Elektronische Ressource]

Notes On Some Inequalities Of P. M. Vasić

Josip E. Pečarić (1980)

Publications de l'Institut Mathématique

Nullstellenverteilung zweier konvexgeometrischer Polynome

J. M. Wills (1989)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

Nuovi risultati sulla semicontinuità inferiore di certi funzionali integrali

Luigi Ambrosio (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Given an open subset $\Omega$ of $\mathbb{R}^{n}$ and a Borel function $f:\Omega\times\mathbb{R}\times\mathbb{R}^{n}\rightarrow[0,+\infty[$ , conditions on $f$ are given which assure the lower semicontinuity of the functional $\int_{\Omega}f(x,u,Du)\,dx$ with respect to different topologies.

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