Strict rearrangement inequalities: nonexpansivity and periodic Gagliardo
seminorms
Strict rearrangement inequalities: nonexpansivity and periodic Gagliardo
seminorms
This paper deals with the behavior of the periodic Gagliardo seminorm under two types of rearrangements, namely under a periodic, and respectively a cylindrical, symmetric decreasing rearrangement. Our two main results are P\'olya-Szeg\H{o} type inequalities for these rearrangements. We also deal with the cases of equality. Our method uses, among …