Sobolev capacity on the space W1, p(⋅)(ℝn)
We define Sobolev capacity on the generalized Sobolev space W1, p(⋅)(ℝn). It is a Choquet capacity provided that the variable exponent p:ℝn→[1,∞) is bounded away from 1 and ∞. We discuss the relation between the Hausdorff dimension and the Sobolev capacity. As another application we study quasiconti...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2003/895261 |
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| Summary: | We define Sobolev capacity on the generalized Sobolev space W1, p(⋅)(ℝn). It is a Choquet capacity provided that the variable exponent p:ℝn→[1,∞) is bounded away from 1 and ∞. We discuss the relation between the Hausdorff dimension and the Sobolev capacity. As another application we study quasicontinuous representatives in the space W1, p(⋅)(ℝn). |
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| ISSN: | 0972-6802 |