Rearrangement in variational inequalities
The authors establish some isoperimetric inequalities for the solution of an obstacle problem in the case the coincidence set reaches the boundary. An optimal lower bound for the measure of the coincidence set is also obtained. The method of proof is based on the technique of rearrangements developed by \textit{G. Talenti} for the Dirichlet problem [Ann. Sc. Norm. Sup. Pisa, Cl. Sci., IV Ser. 3, 697-718 (1976; Zbl 0341.35031)].
scientific article; zbMATH DE number 3897670
scientific article