Brunn-Minkowski inequality for variational functional involving the P-Laplacian operator

In this paper, we investigate the following elliptic problem involving the P-Laplacian (P){-Div(|∇u|p-2∇u)=|u|q-1uinK,u>0inK,u=0onϑK,where p > 1, 0 < q < p − 1, K ⊂ Rn   with K¯∈ Kn, and prove that the energy integral of the problem (P) satisfies a Brunn-Minkowski type inequality.