Oblique derivative problem for quasilinear elliptic equations with VMO coefficients

Strong solvability and uniqueness in the Sobolev space W3,q(Ω), q > n, are proved for the oblique derivative problem ( nΣ i,j=1 a ij(x, u)D iju+b(x, u, Du) = 0 almost everywhere in Ω, δu/δl + σ{x)u =ψ on δΩ, assuming the coefficients of the quasilinear elliptic operator to be Caratheodory functions, a ij ε VMOL ∞ with respect to x, and b to grow at most quadratically with respect to the gradient.