Revisited for existence proof of optimal solution in Bernoulli free boundary problem using an energy-gap cost functional
Abstract
Bernoulli free boundary problem is numerically solved via shape optimization that minimizes a cost functional subject to state problems constraints. In 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 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 Claimed. In this comment, we rectify this proof by Poincar\'e-Friedrichs inequality.
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