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Comparison of Different Definitions of Traces for a Class of Ramified Domains with Self-Similar Fractal Boundaries

Abstract : We consider a class of ramified bidimensional domains with a self-similar boundary, which is supplied with the self-similar probability measure. Emphasis is put on the case when the domain is not an epsilon-delta domain as defined by Jones and the fractal is not totally disconnected.We compare two notions of trace on the fractal boundary for functions in some Sobolev space, the classical one ( the strict definition ) and another one proposed in 2007 and heavily relying on self-similarity. We prove that the two traces coincide almost everywhere with respect to the self similar probability measure.
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https://hal.archives-ouvertes.fr/hal-00657954
Contributor : Maryse Collin <>
Submitted on : Monday, January 9, 2012 - 3:32:20 PM
Last modification on : Thursday, January 7, 2021 - 4:19:15 PM
Long-term archiving on: : Tuesday, April 10, 2012 - 2:35:55 AM

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Yves Achdou, Thibaut Deheuvels, Nicoletta Tchou. Comparison of Different Definitions of Traces for a Class of Ramified Domains with Self-Similar Fractal Boundaries. Potential Analysis, Springer Verlag, 2014, 40 (4), pp.345-362. ⟨10.1007/s11118-013-9352-y⟩. ⟨hal-00657954⟩

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