Strongly nonlinear potential theory on metric spaces
We define Orlicz-Sobolev spaces on an arbitrary metric space with a Borel regular outer measure, and we develop a capacity theory based on these spaces. We study basic properties of capacity and several convergence results. We prove that each Orlicz-Sobolev function has a quasi-continuous representa...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2002-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337502203024 |
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| _version_ | 1832560416616611840 |
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| author | Noureddine Aïssaoui |
| author_facet | Noureddine Aïssaoui |
| author_sort | Noureddine Aïssaoui |
| collection | DOAJ |
| description | We define Orlicz-Sobolev spaces on an arbitrary metric space with
a Borel regular outer measure, and we develop a capacity theory
based on these spaces. We study basic properties of capacity and
several convergence results. We prove that each Orlicz-Sobolev
function has a quasi-continuous representative. We give estimates
for the capacity of balls when the measure is doubling. Under
additional regularity assumption on the measure, we establish
some relations between capacity and Hausdorff measures. |
| format | Article |
| id | doaj-art-d2af666872f248dd955d96711c339a82 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d2af666872f248dd955d96711c339a822025-02-03T01:27:41ZengWileyAbstract and Applied Analysis1085-33751687-04092002-01-017735737410.1155/S1085337502203024Strongly nonlinear potential theory on metric spacesNoureddine Aïssaoui0École Normale Supérieure, B.P. 5206, Ben Souda, Fès, MoroccoWe define Orlicz-Sobolev spaces on an arbitrary metric space with a Borel regular outer measure, and we develop a capacity theory based on these spaces. We study basic properties of capacity and several convergence results. We prove that each Orlicz-Sobolev function has a quasi-continuous representative. We give estimates for the capacity of balls when the measure is doubling. Under additional regularity assumption on the measure, we establish some relations between capacity and Hausdorff measures.http://dx.doi.org/10.1155/S1085337502203024 |
| spellingShingle | Noureddine Aïssaoui Strongly nonlinear potential theory on metric spaces Abstract and Applied Analysis |
| title | Strongly nonlinear potential theory on metric spaces |
| title_full | Strongly nonlinear potential theory on metric spaces |
| title_fullStr | Strongly nonlinear potential theory on metric spaces |
| title_full_unstemmed | Strongly nonlinear potential theory on metric spaces |
| title_short | Strongly nonlinear potential theory on metric spaces |
| title_sort | strongly nonlinear potential theory on metric spaces |
| url | http://dx.doi.org/10.1155/S1085337502203024 |
| work_keys_str_mv | AT noureddineaissaoui stronglynonlinearpotentialtheoryonmetricspaces |