Strong continuity of the relative rearrangement maps and application to a Galerkin approach for nonlocal problems Original Research Article

We study the strong continuity of the map View the MathML source. Here, View the MathML source for σ∈]0 means Ω[, View the MathML source (respectively, (View the MathML source) denotes the decreasing rearrangement of u (respectively b restricted to the set {View the MathML source}) and |E| denotes the Lebesgue measure of a set E included in a domain Ω. The results are useful for solving plasmas physics equations or any nonlocal problems involving the monotone rearrangement, its inverse or its derivatives.