Renormalized solutions of elliptic equations with Robin boundary conditions

In the present paper, we consider elliptic equations with nonlinear and nonhomogeneous Robin boundary conditions of the type

$\{\begin{array}{c}-\text{div}\left(B\left(x,u\right)?u\right)=f\text{in}\Omega ,\\ u=0\text{on}{\Gamma }_o\\ B\left(x,u\right)?u?\overrightarrow{n}+\gamma \left(x\right)h\left(u\right)=g\text{on}{\Gamma }_1\end{array}$

where f and g are the element of L¹ (Ω) and L¹ (Γ₁), respectively. We define a notion of renormalized solution and we prove the existence of a solution. Under additional assumptions on the matrix field B we show that the renormalized solution is unique.