Abstract
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 Lp-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 Ω k and Ω l, the normal vectors at P∈ ∂Ω k and Q∈ ∂Ω l are almost opposite if P and Q are close enough.
Original language | English |
---|---|
Article number | 63 |
Journal | Calculus of Variations and Partial Differential Equations |
Volume | 57 |
Issue number | 2 |
DOIs | |
State | Published - 1 Apr 2018 |
Keywords
- Primary 35K40
- Secondary 35B65