The Poincaré problem in Lp-Sobolev spaces—I: codimension one degeneracy

We study a degenerate oblique derivative problem in Sobolev spaces W2,p( ), ∀p>1, for uniformly elliptic operators with Lipschitz continuous coefficients. The vector field prescribing the boundary condition becomes tangential to at the points of a non-empty set and is of emergent type. © 2005 Elsevier Inc. All rights reserved.