TITLE

A chain rule in $L^{1}\left({\operatorname*{div};\Omega}\right)$ and its applications to lower semicontinuity

AUTHOR(S)
Virginia De Cicco; Giovanni Leoni
PUB. DATE
December 2003
SOURCE
Calculus of Variations & Partial Differential Equations;Dec2003, Vol. 19 Issue 1, p23
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
A chain rule in the space $L^{1}\left(\operatorname*{div};\Omega\right) $ is obtained under weak regularity conditions. This chain rule has important applications in the study of lower semicontinuity problems for general functionals of the form $\int_{\Omega}f(x,u,\nabla u) dx$ with respect to strong convergence in $L^{1}\left(\Omega\right) $ . Classical results of Serrin and of De Giorgi, Buttazzo and Dal Maso are extended and generalized.
ACCESSION #
11657113

 

Related Articles

  • SOME PROPERTIES OF q-BERNSTEIN SCHURER OPERATORS. VEDI, TUBA; ÖZARSLAN, MEHMET ALI // Journal of Applied Functional Analysis;Jan2013, Vol. 8 Issue 1, p45 

    In this paper, we study some shape preserving properties of the q-Bernstein Schurer operators and compute the rate of convergence of these operators by means of Lipschitz class functions, the first and the second modulus of continuity. Furthermore, we give the order of convergence of the...

  • MONOTONE UTILITY CONVERGENCE. Ankirchner, Stefan // Journal of Applied Probability;Sep2006, Vol. 43 Issue 3, p622 

    We show that the maximal expected utility satisfies a monotone continuity property with respect to increasing information. Let (gtn) be a sequence of increasing filtrations converging to (9t∞), and let un(x) and u∞(x) be the maximal expected utilities when investing in a financial...

  • On Beam-like Functions with Radial Symmetry. Papanicolaou, N. C.; Christov, C. I. // AIP Conference Proceedings;10/30/2008, Vol. 1067 Issue 1, p122 

    In this work, we introduce a complete orthonormal (CON) set of functions as the eigenfunctions of a fourth-order boundary problem with radial symmetry. We derive the relation for the spectrum of the problem and solve it numerically. For larger indices n of the eigenvalues we derive accurate...

  • Statistical Approximation of q-Bernstein-Schurer-Stancu-Kantorovich Operators. Qiu Lin // Journal of Applied Mathematics;2014, p1 

    We introduce two kinds of Kantorovich-type q-Bernstein-Schurer-Stancu operators. We first estimate moments of q-Bernstein- Schurer-Stancu-Kantorovich operators. We also establish the statistical approximation properties of these operators. Furthermore, we study the rates of statistical...

  • METHOD WITH A CONTROLLABLE EXPONENTIAL CONVERGENCE RATE FOR NONLINEAR DIFFERENTIAL OPERATOR EQUATIONS. I. P. Gavrilyuk; I. I. Lazurchak; V. L.Makarov; D. Sytnyk // Computational Methods in Applied Mathematics;2009, Vol. 9 Issue 1, p63 

    We propose a new analytical-numerical method with an embedded convergence control mechanism for solving nonlinear operator differential equations. The method provides the exponential convergence rate. A numerical example confirms the theoretical results.

  • ON A SPECIAL SUBCLASS OF THE SET OF DERIVATIVES. Menkyna, Robert // Real Analysis Exchange;2006/2007, Vol. 32 Issue 1, p79 

    We deal with the class of functions defined as a sum of a uniformly convergent series of functions continuous both on a closed set and on its complement. Such functions are mentioned in the literature, e.g., in [1], [2], [3], [4]. We investigate the particular class of derivatives.

  • DIFFERENTIABILITY AS CONTINUITY. Gauld, David; Mynard, Frédéric // Real Analysis Exchange;2005/2006, Vol. 31 Issue 2, p425 

    We characterize differentiability of a map f : ℝ → ℝ in terms of continuity of a canonically associated map f̂. To characterize pointwise differentiability of f, both the domain and range of f̂ can be made topological. However, the global differentiability of f is...

  • Korovkin-type theorem for sequences of operators preserving shape. Sidorov, S. // Positivity;Mar2011, Vol. 15 Issue 1, p11 

    In the paper we present Korovkin-type theorem concerning conditions of convergence sequences of linear operators preserving shape.

  • Weighted Approximation by Analogues of Bernstein Operators for Rational Functions. Dikmen, A.; Lukashov, A. // Acta Mathematica Hungarica;Aug2014, Vol. 143 Issue 2, p439 

    Weighted modifications of generalized Bernstein operators in rational functions (Videnskii operators) are introduced. Their convergence in weighted spaces is studied.

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics