Bogdan Bojarski, Piotr Hajłasz (1993)
Studia Mathematica
We get a class of pointwise inequalities for Sobolev functions. As a corollary we obtain a short proof of Michael-Ziemer’s theorem which states that Sobolev functions can be approximated by functions both in norm and capacity.
Eberhard Schock (1989)
Numerische Mathematik
Jairo Charris, Gustavo Salas, Victoria Silva (1991)
Revista colombiana de matematicas
Crainic, M., Crainic, N. (2010)
Acta Mathematica Universitatis Comenianae. New Series
Achim Clausing (1984)
Mathematische Annalen
Achim Clausing (1984)
Mathematische Annalen
Houman Owhadi, Lei Zhang, Leonid Berlyand (2014)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
We introduce a new variational method for the numerical homogenization of divergence form elliptic, parabolic and hyperbolic equations with arbitrary rough (L∞) coefficients. Our method does not rely on concepts of ergodicity or scale-separation but on compactness properties of the solution space and a new variational approach to homogenization. The approximation space is generated by an interpolation basis (over scattered points forming a mesh of resolution H) minimizing the L2 norm of the source...
Zbigniew Ciesielski, Ryszard Zieliński (2009)
Applicationes Mathematicae
Dvoretzky-Kiefer-Wolfowitz type inequalities for some polynomial and spline estimators of distribution functions are constructed. Moreover, hints on the corresponding algorithms are given as well.
Nirmal Kumar Basu, Madhav Chandra Kundu (1975)
Aplikace matematiky
Ditzian, Z. (2007)
Surveys in Approximation Theory (SAT)[electronic only]
R.M. Aron, J.B. Prolla (1980)
Journal für die reine und angewandte Mathematik
A. Mouze (2010)
Studia Mathematica
We give another version of the recently developed abstract theory of universal series to exhibit a necessary and sufficient condition of polynomial approximation type for the existence of universal elements. This certainly covers the case of simultaneous approximation with a sequence of continuous linear mappings. In the case of a sequence of unbounded operators the same condition ensures existence and density of universal elements. Several known results, stronger statements or new results can be...
Piotr Hajłasz, Agnieszka Kałamajska (1995)
Studia Mathematica
We prove several results concerning density of , behaviour at infinity and integral representations for elements of the space .
Randriambelosoa, Germain E. (2007)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
Eliška Janouchová, Jan Sýkora, Anna Kučerová (2018)
Applications of Mathematics
Recent developments in the field of stochastic mechanics and particularly regarding the stochastic finite element method allow to model uncertain behaviours for more complex engineering structures. In reliability analysis, polynomial chaos expansion is a useful tool because it helps to avoid thousands of time-consuming finite element model simulations for structures with uncertain parameters. The aim of this paper is to review and compare available techniques for both the construction of polynomial...
Mastroianni, G. (2002)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
Mirosław Baran (2015)
Banach Center Publications
We point out relations between the injective complexification of a real Banach space and polynomial inequalities. In particular we prove a generalization of a classical Szegő inequality to the case of polynomial mappings between Banach spaces. As an application we observe a complex version of known Bernstein-Szegő type inequalities.
M. Baran, W. Pleśniak (2000)
Studia Mathematica
We give an estimate of Siciak’s extremal function for compact subsets of algebraic varieties in (resp. ). As an application we obtain Bernstein-Walsh and tangential Markov type inequalities for (the traces of) polynomials on algebraic sets.
Pierre Goetgheluck (1989)
Colloquium Mathematicae
Michael I. Ganzburg (2013)