Recapitulation of some results on relative rearrangement (Q2782328)

The notion of the relative rearrangement of one measurable function with respect to another was introduced by \textit{J. Mossino} and \textit{R. Temam} [Duke Math. J. 48, 475-495 (1981; Zbl 0476.35031)] for the purpose of solving a certain extremal problem arising from plasma physics. Since then, this notion has been studied thoroughly, and has found much application in partial differential equations (including the Navier-Stokes equations) and in the theory of function spaces. The paper under review is a survey of the facts about relative rearrangement. Though it includes little beyond a list of statements, it is useful because many statements are self-explanatory, and a detailed bibliography is included. NEWLINENEWLINENEWLINEFor details, see, e.g., the author and \textit{B. Simon}, Rev. R. Acad. Cienc. Exactas Fis. Nat. (Esp.) 91, No. 1, 17-31, 33-45 (1997; Zbl 0909.35027, Zbl 0909.35028), announced in Appl. Math. Lett. 6, 75-78, 79-82 (1993; Zbl 0781.49024, Zbl 0781.49025).NEWLINENEWLINEFor the entire collection see [Zbl 0978.00050].