Uniqueness for Neumann problems for nonlinear elliptic equations

Abstract

In the present paper we prove uniqueness results for solutions to a class of Neumann boundary value problems whose prototype is    −div((1 + |∇u| 2) (p−2)/2 ∇u) − div(c(x)|u| p−2 u) = f in Ω, (1 + |∇u| 2) (p−2)/2 ∇u + c(x)|u| p−2 u • n = 0 on ∂Ω, where Ω is a bounded domain of R N , N ≥ 2, with Lipschitz boundary, 1 < p < N , n is the outer unit normal to ∂Ω, the datum f belongs to L (p *) (Ω) or to L 1 (Ω) and satisfies the compatibility condition Ω f dx = 0. Finally the coefficient c(x) belongs to an appropriate Lebesgue space.