Relaxation for degenerate nonlinear functionals in the onedimensional case
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916582707429376 |
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| author | Piat, Valeria Chiadò De Cicco, Virginia Hernandez, Anderson Melchor |
| author_facet | Piat, Valeria Chiadò De Cicco, Virginia Hernandez, Anderson Melchor |
| contents | In this study, we approach the analysis of a degenerate nonlinear functional in one dimension, accommodating a degenerate weight $w$. Our investigation focuses on establishing an explicit relaxation formula for a functional exhibiting $p$-growth for $1< p<+\infty$. We adopt the approach developed in [6], where some assumptions like doubling or Muckenhoupt conditions are dropped. Our main tools consist of proving the validity of a weighted Poincaré inequality involving an auxiliary weight. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_02919 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relaxation for degenerate nonlinear functionals in the onedimensional case Piat, Valeria Chiadò De Cicco, Virginia Hernandez, Anderson Melchor Analysis of PDEs 26A15, 49J45 In this study, we approach the analysis of a degenerate nonlinear functional in one dimension, accommodating a degenerate weight $w$. Our investigation focuses on establishing an explicit relaxation formula for a functional exhibiting $p$-growth for $1< p<+\infty$. We adopt the approach developed in [6], where some assumptions like doubling or Muckenhoupt conditions are dropped. Our main tools consist of proving the validity of a weighted Poincaré inequality involving an auxiliary weight. |
| title | Relaxation for degenerate nonlinear functionals in the onedimensional case |
| topic | Analysis of PDEs 26A15, 49J45 |
| url | https://arxiv.org/abs/2404.02919 |