RENORMALIZED SOLUTIONS OF ELLIPTIC EQUATIONS WITH ROBIN BOUNDARY CONDITIONS

摘要

In the present paper, we consider elliptic equations with nonlinear and nonhomogeneous Robin boundary conditions of the type{-div（B（x, u）▽u） = f in ?,u = 0 on Γ0,B（x, u）▽u·n→+γ（x）h（u） =g on Γ1,where f and g are the element of L~1（?） and L~1（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.