Homogenization of Non-Linear Functionals with Laminate-Type Growth

Abstract

<jats:p> The limit energy density, by Γ-convergence, of sequences of functionals whose densities satisfy a growth condition of order <jats:inline-formula> <jats:alternatives> <jats:tex-math notation="LaTeX">p_j(x)</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>p</mml:mi> <mml:mi>j</mml:mi> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> </jats:alternatives> </jats:inline-formula> , depending on the laminate structure of the domain, is computed explicitly through a finite dimensional minimization problem. </jats:p>