Geodesic
On monotonicity of some functionals under monotone rearrangement with respect to one variable
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 45, Tome 444 (2016), pp. 5-14 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the Pólya–Szegö inequality for monotone rearrangement with integrand dependent on the rearrangement variable. The inequality is proved for integrands having polynomial growth. 
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S. V. Bankevich. On monotonicity of some functionals under monotone rearrangement with respect to one variable. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 45, Tome 444 (2016), pp. 5-14. http://geodesic.mathdoc.fr/item/ZNSL_2016_444_a0/

[1] E. Lib, M. Loss, Analiz, Nauchnaya kniga, Novosibirsk, 1998, 276 pp.

[2] B. Kawohl, Rearrangements and convexity of level sets in PDE, Lecture notes in mathematics, 1150, Springer Verlag, Berlin, 1985, 134 pp. | MR | Zbl

[3] F. Brock, “Weighted Dirichlet-type inequalities for Steiner symmetrization”, Calc. Var. and PDEs, 8 (1999), 15–25 | DOI | MR | Zbl

[4] S. V. Bankevich, A. I. Nazarov, “On monotonicity of some functionals under rearrangements”, Calc. Var. and PDEs, 53:3 (2015), 627–647 | DOI | MR | Zbl

[5] S. V. Bankevich, A. I. Nazarov, “Ob obobschenii neravenstva Poia–Sege dlya odnomernykh funktsionalov”, Doklady Akademii Nauk, 438:1 (2011), 11–13 | MR | Zbl

[6] R. Landes, “Some remarks on rearrangements and functionals with non-constant density”, Math. Nachr., 280:5–6 (2007), 560–570 | DOI | MR | Zbl

[7] M. A. Krasnoselskii, P. P. Zabreiko, E. I. Pustylnik, P. E. Sobolevskii, Integralnye operatory v prostranstvakh summiruemykh funktsii, Nauka, M., 1966 | MR