Resumen de Degenerate Elliptic Equations with Nonlinear Boundary Conditions and Measures Data

Fuensanta Andreu Vaíllo , Noureddine Igbida, José Manuel Mazón Ruiz , José Julián Toledo Melero

• In this paper we study the questions of existence and uniqueness of solutions for equations of type −div a(x , Du) + γ (u) 3 µ1 , posed in an open bounded subset Q of RN , with nonlinear boundary conditions of the form a(x , Du)·η +β(u) 3 µ2 . The nonlinear elliptic operator div a(x , Du) is modeled on the p-Laplacian operator tl. p (u) = div (|Du| p−2 Du), with p > 1, γ and β are maximal monotone graphs in R2 such that 0 ∈ γ (0) ∩ β(0) and the data µ1 and µ2 are measures.