A chart preserving the normal vector and extensions of normal derivatives in weighted function spaces

摘要

Given a domain Ω of class C k,1, k ∈ ℕ, we construct a chart that maps normals to the boundary of the half space to normals to the boundary of in the sense that (∂/∂x _n )α(x′, 0) = − N(x′) and that still is of class C k,1. As an application we prove the existence of a continuous extension operator for all normal derivatives of order 0 to k on domains of class C k,1. The construction of this operator is performed in weighted function spaces where the weight function is taken from the class of Muckenhoupt weights. Keywords chart - coordinate transformation - normal vector - normal derivative - extension theorem - Muckenhoupt weight MSC 2000 47A20 - 35A99 - 46E35