On the weakly-* dense subsets in $$$L^{\infty}(\Omega)$$$
Abstract
In this paper we study the density property of the compactly supported smooth functions in the space $$$L^{\infty}(\Omega)$$$. We show that this set is dense with respect to the weak-* convergence in variable spaces.
Full Text:
PDFReferences
Evans L. "Weak Convergence methods for Nonlinear Partial Differential Equations", Reg. Conf. Ser. Math. 74, AMS, 1990.
Valadier M. "Oscillations et compacite forte dans $$$L_1$$$", Sem. Anal. Convexe, 1991; 21, 7.1-7.10. (in French)
Zhikov V.V. "On an extension of the method of two-scale convergence and its applications", Sbornik: Mathematics, 2000; 191(7): pp. 973-1014. doi:10.1070/SM2000v191n07ABEH000491
Zhikov V.V. "Weighted Sobolev spaces", Sbornik: Mathematics, 1998; 189(8): pp. 27-58. doi:10.1070/SM1998v189n08ABEH000344
Zhikov V.V. "Homogenization of elasticity problems on singular structures", Izvestiia: Math., 2002; 66(2): pp. 299-365. doi:10.1070/IM2002v066n02ABEH000380
DOI: https://doi.org/10.15421/240818
Refbacks
- There are currently no refbacks.
Copyright (c) 2008 P.I. Kogut, T.N. Rudyanova
This work is licensed under a Creative Commons Attribution 4.0 International License.