BOUNDARY-VALUE PROBLEM WITH AN OBLIQUE DERIVATIVE FOR UNIFORMLY ELLIPTIC-OPERATORS WITH DISCONTINUOUS COEFFICIENTS

Strong solvability is proved in the Sobolev space W-2,W-p(Omega), 1 < p < infinity, for the regular oblique derivative problem Sigma(i)(j)(n )= 1 a(ij) (x) D(ij)u + Sigma(i)(n) = (1)b(i) (x) D(i)u + c(x)u = f(x) a.e. Omega, partial derivative u/partial derivative l + sigma (x) u = phi (x) on partial derivative Omega, assuming a(ij) is an element of VMO boolean AND L-infinity (Omega), b(i), c is an element of L-q (Omeg a), c less than or equal to 0, sigma less than or equal to 0. Mathemat ics Subject Classification: 35J25, 35R05, 35B45, 35B50.