Regularity and explicit L∞ estimates for a class of nonlinear elliptic systems

Abstract

We use De Giorgi-Nash-Moser iteration scheme to establish that weak solutions to a coupled system of elliptic equations with critical growth on the boundary are in L∞(Ω). Moreover, we provide an explicit L∞(Ω)- estimate of weak solutions with subcritical growth on the boundary, in terms of powers of H1(Ω)-norms, by combining the elliptic regularity of weak solutions with Gagliardo--Nirenberg interpolation inequality.