9.
KHANH Phan Quoc pqkhanh@hcmiu.edu.vn
International University, Vietnam National University Hochiminh City, Vietnam
Titre: Variational convergence of bifunctions on nonrectangular domains and approximations of quasivariational problems (details)
Résumé:
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\centerline{\bf 13th French-Romanian Symposium on Applied Mathematics}
\centerline{\bf Iasi, Romania, August 25-29, 2016}
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\centerline{\large\bf Variational convergence of bifunctions on nonrectangular}
\centerline{\large\bf domains and approximations of quasivariational problems}
\vspace*{0.5cm}\centerline{\bf Phan Quoc Khanh}
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\centerline{International University, Vietnam national University Hochiminh City}
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\noindent{\bf Abstract} \,Variational convergence is a common terminology for kinds of convergence which preserve variational properties such as those about infima, minimizers, infsup-values, minsup-points, saddle values and points, etc. In 2009 Jofre and Wets considered variational convergence of finite-valued bifunctions defined on rectangles instead of defined on the entire product spaces with extended-real-values. Such bifunctions have been proved to be crucial in expressing many variational models in terms of finding minsup- (or maxinf-) points. However, in practice quasivariational problems, i.e., problems with constraint sets depending on their variables, are frequently met. The aim of this paper is to develop epi/hypo and lopsided convergence, the main kinds of variational convergence of bifunctions, to the case of bifunctions defined on nonrectangular domains in order to deal with quasivatiational models. Their basic characterizations are established. Variational properties are proved to be preserved for the limit bifunctions when the bifunctions epi/hypo or lopsided converge (possibly under some additional assumptions). These results are applied to approximations of some typical quasivariational problems. The obtained results are new and, in the special rectangular case, also improve some known results.
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