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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.02702 |
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| _version_ | 1866917059850403840 |
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| author | Wang, Shiouhe Shen, Fang Yang, Yi Feng, Xueshang |
| author_facet | Wang, Shiouhe Shen, Fang Yang, Yi Feng, Xueshang |
| contents | Bernoulli free boundary problem is numerically solved via shape optimization that minimizes a cost functional subject to state problems constraints. In \cite{1}, an energy-gap cost functional was formulated based on two auxiliary state problems, with existence of optimal solution attempted through continuity of state problems with respect to the domain. Nevertheless, there exists a corrigendum in Eq.(48) in \cite{1}, where the boundedness of solution sequences for state problems with respect to the domain cannot be directly estimated via the Cauchy-Schwarz inequality as \textbf{Claimed}. In this comment, we rectify this proof by Poincaré-Friedrichs inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02702 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Revisited for existence proof of optimal solution in Bernoulli free boundary problem using an energy-gap cost functional Wang, Shiouhe Shen, Fang Yang, Yi Feng, Xueshang Analysis of PDEs Solar and Stellar Astrophysics 35R35 (Primary) 35J20 (Secondary) G.1.6; G.1.8 Bernoulli free boundary problem is numerically solved via shape optimization that minimizes a cost functional subject to state problems constraints. In \cite{1}, an energy-gap cost functional was formulated based on two auxiliary state problems, with existence of optimal solution attempted through continuity of state problems with respect to the domain. Nevertheless, there exists a corrigendum in Eq.(48) in \cite{1}, where the boundedness of solution sequences for state problems with respect to the domain cannot be directly estimated via the Cauchy-Schwarz inequality as \textbf{Claimed}. In this comment, we rectify this proof by Poincaré-Friedrichs inequality. |
| title | Revisited for existence proof of optimal solution in Bernoulli free boundary problem using an energy-gap cost functional |
| topic | Analysis of PDEs Solar and Stellar Astrophysics 35R35 (Primary) 35J20 (Secondary) G.1.6; G.1.8 |
| url | https://arxiv.org/abs/2511.02702 |