Pointwise a priori estimates for solution of a system of quasilinear elliptic equation

Abstract

Let B_a⊃Rⁿ be a ball of radius a >2d centered at x₀ and let F be a closed set lying inside the ball B_d of radius d and centered at x₀. For a solution v=(v₁,…,V_N) of the boundary value problem

where e^(j) is a N-dimensional vector whose jth component equals 1 and the remaining components are equal to zero, k is a given real number, we establish the pointwise estimate

for all xεB_a∖B_d.

Keywords:

• Homogenization
• Pointwise estimate
• Quasilinear elliptic system

AMS:

• 35B65
• 35J60

^∗ [email protected]

^∗ [email protected]

Notes

^∗ [email protected]