Korevaar-Schoen $p$-energies and their $Γ$-limits on Cheeger spaces
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929226317299712 |
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| author | Ruiz, Patricia Alonso Baudoin, Fabrice |
| author_facet | Ruiz, Patricia Alonso Baudoin, Fabrice |
| contents | This paper studies properties of $Γ$-limits of Korevaar-Schoen $p$-energies on a Cheeger space. When $p>1$, this kind of limit provides a natural $p$-energy form that can be used to define a $p$-Laplacian, and whose domain is the Newtonian Sobolev space $N^{1,p}$. When $p=1$, the limit can be interpreted as a total variation functional whose domain is the space of BV functions. When the underlying space is compact, the $Γ$-convergence of the $p$-energies is improved to Mosco convergence for every $p \ge 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15699 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Korevaar-Schoen $p$-energies and their $Γ$-limits on Cheeger spaces Ruiz, Patricia Alonso Baudoin, Fabrice Functional Analysis Analysis of PDEs Metric Geometry 30L99, 31C45, 46E36, 47H99 This paper studies properties of $Γ$-limits of Korevaar-Schoen $p$-energies on a Cheeger space. When $p>1$, this kind of limit provides a natural $p$-energy form that can be used to define a $p$-Laplacian, and whose domain is the Newtonian Sobolev space $N^{1,p}$. When $p=1$, the limit can be interpreted as a total variation functional whose domain is the space of BV functions. When the underlying space is compact, the $Γ$-convergence of the $p$-energies is improved to Mosco convergence for every $p \ge 1$. |
| title | Korevaar-Schoen $p$-energies and their $Γ$-limits on Cheeger spaces |
| topic | Functional Analysis Analysis of PDEs Metric Geometry 30L99, 31C45, 46E36, 47H99 |
| url | https://arxiv.org/abs/2401.15699 |