Compactness for $GSBV^p$ via concentration-compactness
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912205690109952 |
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| author | Feldman, William M Stinson, Kerrek |
| author_facet | Feldman, William M Stinson, Kerrek |
| contents | Motivated by variational models for fracture, we provide a new proof of compactness for $GSBV^p$ functions without a priori bounds on the function itself. Our proof is based on the classical idea of concentration-compactness, making it transparent in strategy and simple in implementation. Further, so far as we are aware, this is the first time the connection to concentration-compactness has been made explicit for problems in fracture mechanics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_16308 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Compactness for $GSBV^p$ via concentration-compactness Feldman, William M Stinson, Kerrek Analysis of PDEs 49J45, 70G75, 74B99, 74G65, 74R10 Motivated by variational models for fracture, we provide a new proof of compactness for $GSBV^p$ functions without a priori bounds on the function itself. Our proof is based on the classical idea of concentration-compactness, making it transparent in strategy and simple in implementation. Further, so far as we are aware, this is the first time the connection to concentration-compactness has been made explicit for problems in fracture mechanics. |
| title | Compactness for $GSBV^p$ via concentration-compactness |
| topic | Analysis of PDEs 49J45, 70G75, 74B99, 74G65, 74R10 |
| url | https://arxiv.org/abs/2501.16308 |