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

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dc.contributor.authorTasso, Emanuele
dc.date.accessioned2019-06-27T06:16:52Z
dc.date.available2019-06-27T06:16:52Z
dc.date.issued2019-06
dc.description.abstractIn 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.identifier.urihttps://openscience.sissa.it/handle/1963/35337
dc.language.isoenen_US
dc.publisherSISSAen_US
dc.relation.ispartofseriesSISSA;18/2019/MATE
dc.subjectblow-up, special bounded variationen_US
dc.subjectindecomposable seten_US
dc.subjectjump seten_US
dc.subjectperimeter, rectifiable seten_US
dc.subjectCheeger's constanten_US
dc.subjectisoperimetric profileen_US
dc.subjectPoincare's inequality.en_US
dc.titleOn the blow-up of GSBV functions under suitable geometric properties of the jump seten_US
dc.typePreprinten_US
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