Theory of capacities in fracional Sobolev spaces with variable exponents
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866929538811822080 |
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| author | Baalal, Azeddine Berghout, Mohamed |
| author_facet | Baalal, Azeddine Berghout, Mohamed |
| contents | In this paper we develop a capacities theory connected with the fractional Sobolev spaces with variable exponents. Two kinds of capacities are studied: Sobolev capacity and relative capacity. Basic properties of capacities, including monotonicity, outer capacity and several results, are studies. We prove that both capacities is a Choquet capacity and all borel sets are capacitable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1904_08997 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Theory of capacities in fracional Sobolev spaces with variable exponents Baalal, Azeddine Berghout, Mohamed Functional Analysis Analysis of PDEs In this paper we develop a capacities theory connected with the fractional Sobolev spaces with variable exponents. Two kinds of capacities are studied: Sobolev capacity and relative capacity. Basic properties of capacities, including monotonicity, outer capacity and several results, are studies. We prove that both capacities is a Choquet capacity and all borel sets are capacitable. |
| title | Theory of capacities in fracional Sobolev spaces with variable exponents |
| topic | Functional Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/1904.08997 |