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arXiv · 2511.02702

Revisited for existence proof of optimal solution in Bernoulli free boundary problem using an energy-gap cost functional

Shiouhe Wang·Fang Shen·Yi Yang·Xueshang Feng
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Abstract

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 Poincar\'e-Friedrichs inequality.

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Shiouhe Wang, Fang Shen, Yi Yang, Xueshang Feng. 2025-11-04. Revisited for existence proof of optimal solution in Bernoulli free boundary problem using an energy-gap cost functional. https://arxiv.org/abs/2511.02702

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