Work

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

Year: 2025

Type: preprint

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 Poincaré-Friedrichs inequality.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2511.02702

Authors: Wang, Shiouhe, Shen, Fang, Yang, Yi, Feng, Xueshang

Institutions: National Space Science Center, University of Chinese Academy of Sciences

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Awards: G1110850799, G1225576128, G5252056357

OpenAlex ID: W7103989281

Cites:

Cited by:

Related to: