Global gradient estimates for parabolic systems from composite materials

초록

We obtain global gradient estimates for the weak solutions to parabolic systems from composite materials in Orlicz spaces, which is a new result even for L-p-spaces. We assume that the domain is composed of a finite number of disjoint subdomains with Reifenberg flat boundaries, while the coefficients have small BMO semi-norms in each subdomain and allowed to have big jumps on the boundaries of subdomains. Our proof is based on a new geometric result that for disjoint Reifenberg flat domains Omega(k) and Omega(l), the normal vectors at P is an element of partial derivative Omega(k) and Q is an element of partial derivative Omega(l) are almost opposite if P and Q are close enough.

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