Interpretation of the Lavrentiev phenomenon by relaxation

Abstract: "We consider functionals of the calculus of variations of the form F(u) = [integral]¹₀ f(x,u,u)́ dx defined for u [element of] W[superscript 1,infinity](0,1), and we show that the relaxed functional ⁻F with respect to weak W[superscript 1,1](0,1) convergence can be written as ⁻F(u) = [integral]¹₀ f(x,u,u)́dx + L(u), where the additional term L(u), called the Lavrentiev term, is explicitly identified in terms of F."