Second-order asymptotics of fractional Gagliardo seminorms as $s\to1^-$ and convergence of the associated gradient flows
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917813236531200 |
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| author | Kubin, Andrea Pagliari, Valerio Tribuzio, Antonio |
| author_facet | Kubin, Andrea Pagliari, Valerio Tribuzio, Antonio |
| contents | We study the second-order asymptotic expansion of the $s$-fractional Gagliardo seminorm as $s\to1^-$ in terms of a higher order nonlocal functional. We prove a Mosco-convergence result for the energy functionals and that the $L^2$-gradient flows of the energies converge to the $L^2$-gradient flows of the Mosco-limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17829 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Second-order asymptotics of fractional Gagliardo seminorms as $s\to1^-$ and convergence of the associated gradient flows Kubin, Andrea Pagliari, Valerio Tribuzio, Antonio Analysis of PDEs 49J45, 35R11, 35B40, 45E10, 26A33 We study the second-order asymptotic expansion of the $s$-fractional Gagliardo seminorm as $s\to1^-$ in terms of a higher order nonlocal functional. We prove a Mosco-convergence result for the energy functionals and that the $L^2$-gradient flows of the energies converge to the $L^2$-gradient flows of the Mosco-limit. |
| title | Second-order asymptotics of fractional Gagliardo seminorms as $s\to1^-$ and convergence of the associated gradient flows |
| topic | Analysis of PDEs 49J45, 35R11, 35B40, 45E10, 26A33 |
| url | https://arxiv.org/abs/2410.17829 |