A New Relaxation Space for Obstacles

The space of obstacles (i.e. p-quasi upper semicontinuous functions) is endowed with a distance which is topologically equivalent to the [Gamma]-convergence. We find the metric completion of this space and we give some application for minimization problems of cost functionals depending on obstacles...

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Bibliographic Details
Published in:Acta applicandae mathematicae 2003-12, Vol.79 (3), p.177-194
Main Authors: Bucur, Dorin, Trebeschi, Paola
Format: Article
Language:English
Subjects:
Boundary conditions
Mathematical analysis
Studies
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Summary:The space of obstacles (i.e. p-quasi upper semicontinuous functions) is endowed with a distance which is topologically equivalent to the [Gamma]-convergence. We find the metric completion of this space and we give some application for minimization problems of cost functionals depending on obstacles via their level sets. An element of the completion is a decreasing and [gamma]p-continuous on the left mapping R[contains]t[maps to][mu]t, where [mu]t are positive Borel measures vanishing on sets of zero p-capacity. [PUBLICATION ABSTRACT]
ISSN:0167-8019
1572-9036
DOI:10.1023/B:ACAP.0000003798.03413.67