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Homogenization of non-uniformly bounded periodic diffusion energies in dimension two. (English) Zbl 1221.35048

A homogenization scenario of two-dimensional oscillating convex functionals, where the densities are equicoercive but not uniformly bounded from above, is discussed. Using a couple of technical lemmas and a uniform-convergence result for the minimizers, the authors prove (among other things) that the limit energy is local and recover the validity of the analogue of the well-known periodic homogenization formula.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35J60 Nonlinear elliptic equations
49J45 Methods involving semicontinuity and convergence; relaxation
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