INTERPRETATION OF LAVRENTIEV PHENOMENON BY RELAXATION - THE HIGHER-ORDER CASE

We consider integral functionals of the calculus of variations of the form F(u) = integral(0)(1) f(x, u, u',..., u((n)))dx defined for u is an element of W-n,W-infinity(0, 1), and we show that the relaxed functional (F) over bar with respect to the weak W-loc(n,1)(0, 1) convergence can be written as (F) over bar(u) = integral(0)(1) f(x, u, u',..., u(n))dx + L(u), where the additional term L(u), the Lavrentiev Gap, is explicitly identified in terms of F.