On the location of the maxima in nonlinear Dirichlet problems (Q580585)

In this elegant paper the authors study geometrical properties of the core C(\(\Omega)\) of a convex domain \(\Omega\). They obtain estimates for the location of C(\(\Omega)\) and prove its stability under small deformations of \(\Omega\). They show also that if \(\Omega\) ' is obtained by small enough deformation of a convex \(\Omega\), then C(\(\Omega\) ') is convex. It should be emphasized that in this last result, \(\Omega\) ' need not be convex. The results have application to estimates for solutions of \(\Delta\) u- \(f(u)=0\) in \(\Omega\) under homogeneous Dirichlet data.