Abstract We characterize the trace spaces arising from intersections of weighted, vector-valued Sobolev spaces, where the weights are powers of the distance to the boundary. These weighted function spaces are particularly suitable for treating boundary value problems where derivatives of the solution blow up at the boundary. As an application of our trace theory, we prove well-posedness for the heat equation with rough inhomogeneous boundary data in Sobolev spaces of higher regularity in domains of fixed regularity C^1, C 1, κ, with [0, 1) κ ∈ [ 0, 1).
Denk et al. (Thu,) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: