We consider integral functionals F(u) of the calculus of variations over the integral (0,1), where the integrands is a non autonomous function depending on higher order derivatives. We show that the relaxed functional can be written as F(u)+L(u), where L(u) is the Lavrentiev Gap, which is explicitly identified in terms of F.
Interpretation of Lavrentiev phenomenon by relaxation: the higher order case / Belloni, Marino. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 347:6(1995), pp. 2011-2023. [10.1090/S0002-9947-1995-1290714-9]