Abstract

We prove an homogenization result in W¹,¹ and in BV for a sequence (Fε)(F_\varepsilon) of functionals of the form Fε(u)=∫01f(u/ε,u′) dtF_\varepsilon(u) = \int_0^1 f(u/\varepsilon,u')\,dt where ε is a positive parameter which tends to zero, f : ℝⁿ × ℝⁿ → [0, +∞) is [0, 1)ⁿ-periodic in the first variable, convex in the second variable and satisfies a suitable growth condition of order one. Under the additional assumption that f(x, ·) is positively 1-homogeneous, we show how our result is equivalent to the analogous homogenization result (dealt with by Acerbi and Buttazzo) in which growth conditions of order p > 1 are considered.

Author information

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M. Amar

Dipartimento di Matematica, Università di Pavia, 27100 Pavia, Italy.

E. Vitali

Dipartimento di Matematica, Università di Pavia, 27100 Pavia, Italy

Keywords

  • Homogenization
  • Γ-convergence
  • BV-functions

References

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Suggested citation

M. Amar, E. Vitali. “Homogenization of Periodic Finsler Metrics.” Journal of Convex Analysis 5 (1998), No. 1, 171–186. https://doi.org/10.68381/jca05-13

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Published by Heldermann Verlag, 1998. Rights now held by Banach Press LLC.