A density result in Sobolev spaces. (Q1406907)

Let \(\Omega\) be an open set in \(\mathbb{R}^n\). The author considers the problem of the density of ``nice'' functions, satisfying the Neumann boundary condition, in the Sobolev space \(W^{1,p}(\Omega)\). He proves two theorems on this density, one for the case of polygonal sets which have Lipschitz boundary contained in a finite union of hyperplanes, and another one for regular domains. Some applications to the so-called finite volume schemes for diffusion problems are discussed, and a generalization to the case of mixed Dirichlet-Neumann boundary conditions is also developed.