TY - JOUR

T1 - Lp gradient estimate for elliptic equations with high-contrast conductivities in Rn

AU - Yeh, Li-Ming

PY - 2016/7/15

Y1 - 2016/7/15

N2 - Uniform estimate for the solutions of elliptic equations with high-contrast conductivities in Rn is concerned. The space domain consists of a periodic connected sub-region and a periodic disconnected matrix block subset. The elliptic equations have fast diffusion in the connected sub-region and slow diffusion in the disconnected subset. Suppose ε∈(0, 1] is the diameter of each matrix block and ω2∈(0, 1] is the conductivity ratio of the disconnected matrix block subset to the connected sub-region. It is proved that the W1,p norm of the elliptic solutions in the connected sub-region is bounded uniformly in ε, ω when ε≤ω, the Lp norm of the elliptic solutions in the whole space is bounded uniformly in ε, ω the W1,p norm of the elliptic solutions in perforated domains is bounded uniformly in ε. However, the Lp norm of the second order derivatives of the solutions in the connected sub-region may not be bounded uniformly in ε, ω.

AB - Uniform estimate for the solutions of elliptic equations with high-contrast conductivities in Rn is concerned. The space domain consists of a periodic connected sub-region and a periodic disconnected matrix block subset. The elliptic equations have fast diffusion in the connected sub-region and slow diffusion in the disconnected subset. Suppose ε∈(0, 1] is the diameter of each matrix block and ω2∈(0, 1] is the conductivity ratio of the disconnected matrix block subset to the connected sub-region. It is proved that the W1,p norm of the elliptic solutions in the connected sub-region is bounded uniformly in ε, ω when ε≤ω, the Lp norm of the elliptic solutions in the whole space is bounded uniformly in ε, ω the W1,p norm of the elliptic solutions in perforated domains is bounded uniformly in ε. However, the Lp norm of the second order derivatives of the solutions in the connected sub-region may not be bounded uniformly in ε, ω.

KW - Duality argument

KW - Embedding theory

KW - High-contrast conductivity

KW - Potentials

UR - http://www.scopus.com/inward/record.url?scp=84962636405&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2016.03.027

DO - 10.1016/j.jde.2016.03.027

M3 - Article

AN - SCOPUS:84962636405

VL - 261

SP - 925

EP - 966

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 2

ER -