Publicação
The fractal Dirichlet Laplacian
| dc.contributor.author | Caetano, António M. | |
| dc.contributor.author | Lopes, Sofia | |
| dc.date.accessioned | 2026-01-19T11:19:19Z | |
| dc.date.available | 2026-01-19T11:19:19Z | |
| dc.date.issued | 2010-04-09 | |
| dc.description.abstract | An h-set is a non-empty compact subset of the Euclidean n-space which supports a finite Radon measure for which the measure of balls centered on the subset is essentially given by the image of their radius by a suitable function h. In most cases of interest such a subset has Lebesgue measure zero and has a fractal structure. We prove the existence of solutions for the so-called fractal Dirichlet problem for such h-sets. The “construction” of the solutions is based on the consideration of complete o.n. systems for convenient function spaces on the fractals. These systems are obtained combining properties of traces with integral representations (obtained with the help of Green’s functions) for the so-called fractal Laplacian. | eng |
| dc.description.sponsorship | The authors would like to thank Prof. Hans Triebel for his valuable suggestions and for the fruitful discussions during the preparation of this paper. This research was partially supported by Unidade de Investigação Matemática e Aplicações of Uni versidade de Aveiro through Programa Operacional ‘Ciência, Tecnologia, Inovação’ (POCTI) of FCT, cofinanced by the European Community Fund (FEDER). | |
| dc.identifier.citation | Caetano, A.M., Lopes, S. The fractal Dirichlet Laplacian. Rev Mat Complut 24, 189–209 (2011). https://doi.org/10.1007/s13163-010-0035-6 | |
| dc.identifier.doi | 10.1007/s13163-010-0035-6 | |
| dc.identifier.issn | 1139-1138 | |
| dc.identifier.issn | 1988-2807 | |
| dc.identifier.uri | http://hdl.handle.net/10400.8/15389 | |
| dc.language.iso | eng | |
| dc.peerreviewed | yes | |
| dc.publisher | Springer Science and Business Media LLC | |
| dc.relation.hasversion | https://link.springer.com/article/10.1007/s13163-010-0035-6 | |
| dc.relation.ispartof | Revista Matemática Complutense | |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | |
| dc.subject | Traces | |
| dc.subject | h-sets · | |
| dc.subject | Laplacian · | |
| dc.subject | Dirichlet problem · | |
| dc.subject | Function spaces · | |
| dc.subject | Fractals · | |
| dc.title | The fractal Dirichlet Laplacian | eng |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.citation.endPage | 209 | |
| oaire.citation.issue | 1 | |
| oaire.citation.startPage | 189 | |
| oaire.citation.title | Revista Matematica Complutense | |
| oaire.citation.volume | 24 | |
| oaire.version | http://purl.org/coar/version/c_970fb48d4fbd8a85 |