Journal of the
Korean Mathematical Society JKMS

We prove the global regularity of weak solutions to a conormal derivative boundary value problem for quasilinear elliptic equations in divergence form on Lipschitz domains under the controlled growth conditions on the low order terms. The leading coefficients are in the class of BMO functions with small mean oscillations.

Keywords: quasilinear elliptic equations, conormal derivative boundary value problem, BMO coefficients, Sobolev spaces

MSC numbers: 35J62, 35J25, 35B65