Nonlocal problems in thin domains

We also study a nonlocal Dirichlet problem f(x)=∫RNJϵ(x−y)(uϵ(y)−uϵ(x))dy, x∈Ω, with uϵ(x)≡0, x∈RN∖Ω, and deal with similar issues. In this case the limit as ϵ→0 is u0=0 and the double limit problem commutes and also gives v≡0 at the end.