# Global gradient estimates for parabolic systems from composite materials

Global gradient estimates for parabolic systems from composite materials 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 $$L^{p}$$ 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 $$\Omega ^{k}$$ Ω k and $$\Omega ^{l}$$ Ω l , the normal vectors at $$P \in \partial \Omega ^{k}$$ P ∈ ∂ Ω k and $$Q \in \partial \Omega ^{l}$$ Q ∈ ∂ Ω l are almost opposite if P and Q are close enough. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Calculus of Variations and Partial Differential Equations Springer Journals

# Global gradient estimates for parabolic systems from composite materials

, Volume 57 (2) – Mar 14, 2018
18 pages

Publisher
Springer Berlin Heidelberg
Subject
Mathematics; Analysis; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Theoretical, Mathematical and Computational Physics
ISSN
0944-2669
eISSN
1432-0835
D.O.I.
10.1007/s00526-018-1330-1
Publisher site
See Article on Publisher Site

### 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 $$L^{p}$$ 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 $$\Omega ^{k}$$ Ω k and $$\Omega ^{l}$$ Ω l , the normal vectors at $$P \in \partial \Omega ^{k}$$ P ∈ ∂ Ω k and $$Q \in \partial \Omega ^{l}$$ Q ∈ ∂ Ω l are almost opposite if P and Q are close enough.

### Journal

Calculus of Variations and Partial Differential EquationsSpringer Journals

Published: Mar 14, 2018

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