ABSTRACT
This is a technical chapter that will ease the way to constructing the trace operator in Chapter 4, our main obstacle in the pursuit of the analysis of nonhomogeneous Dirichlet boundary conditions for elliptic problems. We will prepare the way by dealing with four issues:
Proving that the Sobolev spaces H 1 are mapped naturally to each other under Lipschitz changes of variables.
Setting up a class of domains on which we will be able to handle nonhomogeneous boundary conditions for elliptic PDE.
Preparing access to information close to the boundary on the said domains by organizing a set of charts, a cover of the boundary, and an associated partition of unity.
Describing integration on the boundary of a Lipschitz domain.
