1308.0963 (Martin Jesenko et al.)

Closure and commutability results for Gamma-limits and the geometric
linearization and homogenization of multi-well energy functionals    [PDF]

Martin Jesenko, Bernd Schmidt

Under a suitable notion of equivalence of integral densities we prove a $\Gamma$-closure theorem for integral functionals: The limit of a sequence of $\Gamma$-convergent families of such functionals is again a $\Gamma$-convergent family. Its $\Gamma$-limit is the limit of the $\Gamma$-limits of the original problems. This result not only provides a common basic principle for a number of linearization and homogenization results in elasticity theory. It also allows for new applications as we exemplify by proving that geometric linearization and homogenization of multi-well energy functionals commute.

View original: http://arxiv.org/abs/1308.0963