A second order Bourgain-Brézis-Mironescu type formula in Euclidean domains

In arbitrary Euclidean domains, we build up a second order BBM type formula, that is, as \texts\rightarrow 2^- , we obtained the convergence from s-order intrinisic Triebel-Lizorkin type (semi-)norm defined via 2-order difference to an equivalence of second order Sobolev (semi-)norm.