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- Title
On the Fenchel–Moreau conjugate of G-function and the second derivative of the modular in anisotropic Orlicz spaces.
- Authors
Maksymiuk, Jakub
- Abstract
In this paper, we investigate the properties of the Fenchel–Moreau conjugate of G-function with respect to the coupling function c (x , A) = | A [ x ] 2 | . We provide conditions that guarantee that the conjugate is also a G-function. We also show that if a G-function G is twice differentiable and its second derivative belongs to the Orlicz space generated by the Fenchel–Moreau conjugate of G then the modular generated by G is twice differentiable on the Orlicz space generated by G. We also investigate second-order differentiability of action functionals on anisotropic Orlicz–Sobolev spaces.
- Subjects
ORLICZ spaces; FUNCTIONALS
- Publication
Calculus of Variations & Partial Differential Equations, 2024, Vol 63, Issue 2, p1
- ISSN
0944-2669
- Publication type
Article
- DOI
10.1007/s00526-023-02655-8