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Annali di Matematica Pura ed Applicata

, Volume 117, Issue 1, pp 139–152 | Cite as

Periodic solutions and homogenization of non linear variational problems

  • Paolo Marcellini
Article

Summary

We prove an homogenization formula for some non linear variational problems that extends the analogous one known in the linear case. Namely the solution uε of the problem
$$\int\limits_\Omega {\left\{ {f\left( {\frac{x}{\varepsilon },Du_\varepsilon } \right) - \varphi \left( x \right)u_\varepsilon } \right\}dx} = minimum,$$
where the boundary data are independent of ɛ and f=f(x, ξ) is periodic in x, converges in some Lp space as ɛ goes to zero to the solution of an analogous variational problem whose integrand can be evaluated from f.

Keywords

Periodic Solution Variational Problem Boundary Data Linear Case Homogenization Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Nicola Zanichelli Editore 1978

Authors and Affiliations

  • Paolo Marcellini
    • 1
  1. 1.Firenze

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