Maximal monotonicity for the sum of two subdifferential operators in LpLp-spaces

This paper is devoted to providing a sufficient condition for the maximality of the sum of subdifferential operators defined on reflexive Banach spaces and proving the maximal monotonicity in Lp(Ω)×Lp′(Ω)Lp(Ω)×Lp′(Ω) of the nonlinear elliptic operator u↦−Δmu+β(u(⋅))u↦−Δmu+β(u(⋅)) with a maximal monotone graph ββ.