## Interpretation of Lavrentiev phenomenon by relaxation: the higher order case

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**347**(1995), 2011-2023 Request permission

## Abstract:

We consider integral functionals of the calculus of variations of the form \[ F(u) = \int \limits _0^1 {f(x,u,u’, \ldots ,{u^{(n)}})dx} \] defined for $u \in {W^{n,\infty }}(0,1)$, and we show that the relaxed functional $F$ with respect to the weak $W_{{\text {loc}}}^{n,1}(0,1)$ convergence can be written as \[ \overline F (u) = \int \limits _0^1 {f(x,u,u’, \ldots ,{u^{(n)}})dx + L(u),} \] where the additional term $L(u)$, the Lavrentiev Gap, is explicitly identified in terms of $F$.## References

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## Additional Information

- © Copyright 1995 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**347**(1995), 2011-2023 - MSC: Primary 49J45; Secondary 49J05
- DOI: https://doi.org/10.1090/S0002-9947-1995-1290714-9
- MathSciNet review: 1290714