%0 Journal Article
%T Schwarz rearrangement does not decrease the energy for the pseudo p-Laplacian operator
%A Mohammed MOUSSA
%J Boletim da Sociedade Paranaense de Matem¨¢tica
%D 2011
%I Sociedade Brasileira de Matem¨¢tica
%X It is well known that the Schwarz symmetrization decrease the energyfor the p-Laplacian operator, i.eint_{overline{Omega}}| u|^p dx ¡Ý int_{overline{Omega^*}}| u^ |p dx,where u  is the Schwarz rearranged function of u, for appropriate u and Omega. In this note, we shall proof that the Schwarz rearrangement does not decrease the energy for the pseudo p-Laplacian operator, that is, there exist a bounded domain Omega   R^N and a function u ¡Ê W_0^{1,p}(Omega)such thatint_{Omega^*}sum_{i=1}^N |partial_{x_i}u^*|^p dx geq int_{Omega}sum_{i=1}^N |partial_{x_i}u|^p dx.
%K Schwarz symmetrization
%K pseudo p-Laplacian operator.
%U http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/10428/6195