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

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