A mathematical programming problem with singular mixed pointwise-integral constraints

We investigate an infinite dimensional optimization problem which constraints are singular integral-pointwise ones. We give some partial results of existence for a solution in some particular cases. However, the lack of compactness, even in L 1 prevents to conclude in the general case. We give an ex...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2005-08, Vol.308 (2), p.491-512
Main Authors: Bergounioux, Maïtine, Maheux, Patrick
Format: Article
Language:English
Subjects:
Calculus of variations and optimal control
Compactness
Exact sciences and technology
Mathematical analysis
Mathematics
Measure
Minimization
Optimization and Control
Sciences and techniques of general use
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Summary:We investigate an infinite dimensional optimization problem which constraints are singular integral-pointwise ones. We give some partial results of existence for a solution in some particular cases. However, the lack of compactness, even in L 1 prevents to conclude in the general case. We give an existence result for a weak solution (as a measure) that we are able to describe. The regularity of such a solution is still an open problem.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2004.11.020