Uniqueness for Neumann problems for nonlinear elliptic equations

UNIQUENESS FOR NEUMANN PROBLEMS FOR NONLINEAR ELLIPTIC EQUATIONS

Maria Francesca F Betta (1) , Olivier Guibé (2) , Anna Mercaldo (3)

1 Dipartimento per le Tecnologie Universita degli studi di Napoli Parthenope
2 LMRS - Laboratoire de Mathématiques Raphaël Salem
3 University of Naples Federico II = Università degli studi di Napoli Federico II

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,

Mots clés: renormalized solutions; Neumann problems; nonlinear elliptic equations; uniqueness

Domaines: Equations aux dérivées partielles [math.AP]

Maria Francesca F Betta, Olivier Guibé, Anna Mercaldo. Uniqueness for Neumann problems for nonlinear elliptic equations. Communications in Pure and Applied Analysis, 2019, ⟨10.3934/cpaa.2019050⟩. ⟨hal-01659249⟩