Optimization of the energy integral in two classes ofrearrangements

摘要

This paper concerns the maximization and the minimization of the energy integral associated to asecond order elliptic problem in classes of rearrangements with respect to either the Lebesgue measure or to ameasure related to the structure of the equation. We find results of existence, uniqueness and representationof the maximizers and the minimizers. Precise characterizations of the optimizers are found in case thedomain is a ball. Finally, the effect of special geometrical transformations concerning these problems isdiscussed.