A stability result for nonlinear Neumann problems under boundary variations

AbstractIn this paper we study, in dimension two, the stability of the solutions of some nonlinear elliptic equations with Neumann boundary conditions, under perturbations of the domains in the Hausdorff complementary topology. More precisely, for every bounded open subset Ω of R2, we consider the problem: −diva(x,∇uΩ)+b(x,uΩ)=0inΩ,a(x,∇uΩ)·ν=0on∂Ω, where a:R2×R2→R2 and b:R2×R→R are two Carathéodory functions which satisfy the standard monotonicity and growth conditions of order p, with 1