We study an elliptic operator L: =div (A) on the upper half space. It is known that if the matrix A is independent in the transversal t-direction, then the regularity boundary value problem is solvable with data in a Sobolev space. In the present paper we improve on the t-independence condition by introducing a mixed L¹-L^ condition that only depends on ₜ A, the derivative of A in transversal direction. This condition is different from other conditions in the literature and has already been proven to imply solvability of the Dirichlet boundary value problem.
Martin Ulmer (Wed,) studied this question.