Homogenization for Non Linear Elliptic Equations with Random Highly Oscillatory Coefficients
Alain Bensoussan · Birkhäuser Boston eBooks · 1989
We consider in this article non linear elliptic equations of the form $$\eqalign{ & - {\partial \over {\partial {x_i}}}(a_{ij}^ \in (x;\omega ){{\partial {u^ \in }} \over {\partial {x_j}}}) = {H^ \in }(x,D{u^ \in },{u^ \in },\omega ),{\rm{ }}x \in O \cr & {\rm{ u }}_{\rm{|}}^ \in \partial o = 0 \cr} $$ where a ∊ i j(x;ω) is a sequence of stochastic processes, the matrix a ∊ i j being uniformly bounded and coercive. The non linear operator H ∊ has quadratic growth in Du ∊.