Yichen Liu, Mohsen Zivari-Rezapour, Behrouz Emamizadeh
Abstract:
We develop the rearrangement optimization theory in the setting of Orlicz spaces.
By using this theory, we can investigate the rearrangement minimization and
maximization problems related to the boundary value problems containing the
\(\Phi\)-Laplacian and the \(\Phi\)-Kirchhoff operator separately.
We show the existence of solutions and derive the corresponding optimality
conditions for both the minimization and maximization problems.
For the maximization problems, we also prove the uniqueness of solutions.
Submitted November 2, 2023. Published August 18, 2026.
Math Subject Classifications: 35J25, 35J20, 49K20, 46E30.
Key Words: Orlicz space; optimization; rearrangements of functions.
DOI: 10.58997/ejde.2026.62
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Yichen Liu Department of Applied Mathematics School of Mathematics and Physics Xi'an Jiaotong-Liverpool University Suzhou, China mail: Yichen.Liu01@xjtlu.edu.cn |
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Mohsen Zivari-Rezapour Department of Mathematics Faculty of Mathematical Sciences and Computer Shahid Chamran University of Ahvaz Ahvaz, Iran mail: mzivari@scu.ac.ir |
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Behrouz Emamizadeh Department of Mathematical Sciences University of Nottingham, Ningbo, China mail: Behrouz.Emamizadeh@nottingham.edu.cn, Behrouz.Emamizadeh@ipm.ir |
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