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2017•Discrete and Continuous Dynamical SystemsOpen access

Regularity of elliptic systems in divergence form with directional homogenization

Rong Dong, Dongsheng Li, Lihe Wang

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Abstract

In this paper, we study regularity of solutions of elliptic systems in divergence form with directional homogenization. Here directional homogenization means that the coefficients of equations are rapidly oscillating only in some directions. We will investigate the different regularity of solutions on directions with homogenization and without homogenization. Actually, we obtain uniform interior $W^{1, p}$ estimates in all directions and uniform interior $C^{1, γ}$ estimates in the directions without homogenization.

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What this paper is about

In this paper, we study regularity of solutions of elliptic systems in divergence form with directional homogenization. Here directional homogenization means that the coefficients of equations are rapidly oscillating only in some directions. We will investigate the different regularity of solutions on directions with homogenization and without homogenization. Actually, we obtain uniform interior $W^{1, p}$ estimates in all directions and uniform interior $C^{1, γ}$ estimates in the directions without homogenization.

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Available abstract

In this paper, we study regularity of solutions of elliptic systems in divergence form with directional homogenization. Here directional homogenization means that the coefficients of equations are rapidly oscillating only in some directions. We will investigate the different regularity of solutions on directions with homogenization and without homogenization. Actually, we obtain uniform interior $W^{1, p}$ estimates in all directions and uniform interior $C^{1, γ}$ estimates in the directions without homogenization.

Key concepts: Homogenization (climate), Mathematics, Mathematical analysis, Biodiversity, Biology, Ecology

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