No abstract

We study the conormal derivative problem for an elliptic equation of p-Laplacian type with discontinuous coefficients in a non-smooth domain in order to look for the minimal assumptions necessary to have the nonlinear Calderón-Zygmund theory for such problem. Under the assumptions that the nonlinear operator is sufficiently close to the p-Laplacian operator in BMO semi-norm and the boundary of the domain can be locally approximated by the convex boundary, we prove that both the gradient and the associated nonhomogeneous term belong to the same L q space for every q ∈ [p, ∞). As far as the domain is concerned, our regularity assumption on the boundary is weaker than any other one reported in this direction.

In the above article [1] the funding information was missing. Please find it below.