A CHART PRESERVING THE NORMAL VECTOR ANDEXTENSIONS OF NORMAL DERIVATIVES IN WEIGHTEDFUNCTION SPACES

摘要

Given a domain ft of class Ck,1, k ∈ N, we construct a chart that mapsnormals to the boundary of the half space to normals to the boundary of Ω in the sensethat (/xn)α(x' , 0) = -N(x') and that still is of class Ck'1. As an application we provethe existence of a continuous extension operator for all normal derivatives of order 0 to k ondomains of class Ck,1. The construction of this operator is performed in weighted functionspaces where the weight function is taken from the class of Muckenhoupt weights.