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

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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. 
@article{ZNSL_2016_444_a0,
     author = {S. V. Bankevich},
     title = {On monotonicity of some functionals under monotone rearrangement with respect to one variable},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--14},
     publisher = {mathdoc},
     volume = {444},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_444_a0/}
}
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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/