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On the blow-up of GSBV functions under suitable geometric properties of the jump set

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dc.contributor.author Tasso, Emanuele
dc.date.accessioned 2019-06-27T06:16:52Z
dc.date.available 2019-06-27T06:16:52Z
dc.date.issued 2019-06
dc.identifier.uri http://preprints.sissa.it:8180/xmlui/handle/1963/35337
dc.description.abstract In this paper we investigate the fine properties of functions under suitable geometric conditions on the jump set. Precisely, given an open set Ω С Rn and given p > 1 we study the blow-up of functions u Є2 GSBV (Ω), whose jump sets belongs to an appropriate class Jp and whose approximate gradient is p-th power summable. In analogy with the theory of p-capacity in the context of Sobolev spaces, we prove that the blow-up of u converges up to a set of Hausdorff dimension less than or equal to n - p. Moreover, we are able to prove the following result which in the case of W1,p (Ω) functions can be stated as follows: whenever uk strongly converges to u, then up to subsequences, uk pointwise converges to u except on a set whose Hausdorff dimension is at most n - p.
dc.language.iso en en_US
dc.publisher SISSA en_US
dc.relation.ispartofseries SISSA;18/2019/MATE
dc.subject blow-up, special bounded variation en_US
dc.subject indecomposable set en_US
dc.subject jump set en_US
dc.subject perimeter, rectifiable set en_US
dc.subject Cheeger's constant en_US
dc.subject isoperimetric profile en_US
dc.subject Poincare's inequality. en_US
dc.title On the blow-up of GSBV functions under suitable geometric properties of the jump set en_US
dc.type Preprint en_US


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