Conductive Homogeneity of Compact Metric Spaces and Construction of 𝑝-Energy
In the ordinary theory of Sobolev spaces on domains of , the -energy is defined as the integral of ||. In this paper, we try to construct a -energy on compact metric spaces as a scaling limit of discrete -energies on a series of graphs approximating the original space. In conclusion, we propose a no...
Sparad:
| Huvudupphovsman: | |
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| Materialtyp: | Livre numérique |
| Språk: | Anglais |
| Publicerad: |
Berlin :
European Mathematical Society
2023.
Berlin : |
| Serie: | Memoirs of the European Mathematical Society
5 |
| Länkar: | Accès sur la plateforme EMS Press Accès sur la plateforme ISTEX Accès Université d'Orléans Accès INSA CVL |
| Anmärkning: |
European Mathematical Society (Licence nationale) European Mathematical Society (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Conductive Homogeneity of Compact Metric Spaces and Construction of 𝑝-Energy, 978-3-98547-056-3 |
| Sammanfattning: | In the ordinary theory of Sobolev spaces on domains of , the -energy is defined as the integral of ||. In this paper, we try to construct a -energy on compact metric spaces as a scaling limit of discrete -energies on a series of graphs approximating the original space. In conclusion, we propose a notion called conductive homogeneity under which one can construct a reasonable -energy if p is greater than the Ahlfors regular conformal dimension of the space. In particular, if 2, then we construct a local regular Dirichlet form and show that the heat kernel associated with the Dirichlet form satisfies upper and lower sub-Gaussian type heat kernel estimates. As examples of conductively homogeneous spaces, we present new classes of square-based self-similar sets and rationally ramified Sierpiński crosses, where no diffusions were constructed before. |
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| Beskrivning: | European Mathematical Society (Licence nationale) European Mathematical Society (Licence nationale) |
| ISBN: | 9783985475568 |
| ISSN: | 2747-9099 |
| Tillgång: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences Accès libre en ligne à l'intégralité de la ressource |