Kevin Brewster and Marius Mitrea

Boundary Value Problems in Weighted Sobolev Spaces on Lipschitz Manifolds

We explore the extent to which well-posedness results for the Poisson problem with a Dirichlet boundary condition hold in the setting of weighted Sobolev spaces in rough settings. The latter includes both the case of (strongly and weakly) Lipschitz domains in an Euclidean ambient, as well as compact Lipschitz manifolds with boundary.

Mathematics Subject Classification: Primary 42B35, 35J58; Secondary 46B70, 46E35

Key words and phrases: Higher-order Sobolev space, linear extension operator, boundary trace operator, complex interpolation, weighted Sobolev space, Besov space, boundary value problem, Poisson problem with Dirichlet boundary condition, strongly elliptic system, strongly Lipschitz domain, weakly Lipschitz domain, compact Lipschitz manifold with boundary