Comparison of Different Definitions of Traces for a Class of Ramified Domains with Self-Similar Fractal Boundaries
Overview & Synopsis
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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Document Information
| Document Title | Comparison of Different Definitions of Traces for a Class of Ramified Domains with Self-Similar Fractal Boundaries |
|---|---|
| Author / Organization | Yves Achdou, Thibaut Deheuvels, Nicoletta Tchou |
| Subject & Discipline | Multidisciplinary Academic Open Research |
| Categories | Science & Mathematics |
| Publication Year | 2014 |
| License / Rights | Open Access / Creative Commons |
| Resource Verification | Listed PDF (Verification Pending) |
| Original Host Website |
HAL Open Science
(hal.science)
|
| File Format | application/pdf (Portable Document Format) |
| Language | EN |
| Catalog ID | DOC-18684 |
| Original Source Link | Visit Source Page on hal.science » |