Uniform Elliptic Estimate for an Infinite Plate in Linear Elasticity

Abstract

We present a new study of linear elasticity for an infinite three-dimensional plate of finite thickness Ω = ?² × (?1, 1). We first characterize the kernel of the operator of elasticity as polynomials which can be build from the kernel of the classical Kirchhoff–Love model of plate. Using this characterization, we get optimal uniform elliptic estimates W ^{k, p} , C ^{k, α} on the solution as a function of the exterior forces. We also give an interior estimate.