Minimization of Degenerate Nonlinear Functionals under Radial Symmetry
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915414234103808 |
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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 work, we study the minimization of nonlinear functionals in dimension $d\geq 1$ that depend on a degenerate radial weight $w$. Our goal is to prove the existence of minimizers in a suitable functional class here introduced and to establish that the minimizers of such functionals, which exhibit $p$-growth with $1 < p < +\infty$, are radially symmetric. In our analysis, we adopt the approach developed in [Chiadò Piat, De Cicco and Melchor Hernandez, NoDEA $2025$, De Cicco and Serra Cassano, ESAIM:COCV $2024$], where $w$ does not satisfy classical assumptions such as doubling or Muckenhoupt conditions. The core of our method relies on proving the validity of a weighted Poincaré inequality involving a suitably constructed auxiliary weight. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20603 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimization of Degenerate Nonlinear Functionals under Radial Symmetry Piat, Valeria Chiadò De Cicco, Virginia Hernandez, Anderson Melchor Analysis of PDEs Functional Analysis 26A15, 49J45 In this work, we study the minimization of nonlinear functionals in dimension $d\geq 1$ that depend on a degenerate radial weight $w$. Our goal is to prove the existence of minimizers in a suitable functional class here introduced and to establish that the minimizers of such functionals, which exhibit $p$-growth with $1 < p < +\infty$, are radially symmetric. In our analysis, we adopt the approach developed in [Chiadò Piat, De Cicco and Melchor Hernandez, NoDEA $2025$, De Cicco and Serra Cassano, ESAIM:COCV $2024$], where $w$ does not satisfy classical assumptions such as doubling or Muckenhoupt conditions. The core of our method relies on proving the validity of a weighted Poincaré inequality involving a suitably constructed auxiliary weight. |
| title | Minimization of Degenerate Nonlinear Functionals under Radial Symmetry |
| topic | Analysis of PDEs Functional Analysis 26A15, 49J45 |
| url | https://arxiv.org/abs/2507.20603 |