On the relaxation of variational integrals in metric Sobolev spaces
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AbstractWe give an extension of the theory of relaxation of variational integrals in classical Sobolev spaces to the setting of metric Sobolev spaces. More precisely, we establish a general framework to deal with the problem of finding an integral representation for “relaxed” variational functionals of variational integrals of the calculus of variations in the setting of metric measure spaces. We prove integral representation theorems, both in the convex and non-convex case, which extend and complete previous results in the setting of euclidean measure spaces to the setting of metric measure spaces. We also show that these integral representation theorems can be applied in the setting of Cheeger–Keith's differentiable structure.
2006 ◽
Vol 36
(0)
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pp. 79-94
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2010 ◽
Vol 55
(1-3)
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pp. 253-267
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2018 ◽
Vol 20
(07)
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pp. 1750077
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2017 ◽
Vol 10
(4)
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pp. 381-405
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2019 ◽
Vol 475
(2223)
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pp. 20180310
2015 ◽
Vol 65
(2)
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pp. 435-474
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