Compactness of minimizing sequences. (May 2016)

• Record Type: Journal Article
• Authors: Boccardo, Lucio; Gallouet, Thierry
• Is Part Of: Nonlinear analysis. Volume 137(2016)
• Page Start: 213
• Page End: 221
• Publication Date: 2016-05
• Subjects: Minimizing sequences -- Compactness; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.12.023
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider a minimization problem of a functional in the space W 0 1, p ( Ω ), where 1 < p < + ∞ and Ω is a bounded open set of R N . We prove the compactness, in the space W 0 1, p ( Ω ), under convenient hypotheses, of a minimizing sequence. The main difficulty is to prove the convergence in measure of the gradient of the minimizing sequence. Furthermore, considering a sequence of minimization problems in the space W 0 1, p ( Ω ), we prove some convergence results of the sequence of minimizers to the minimizer of the limit problem.