Boundedness of weak solutions of degenerate quasilinear equations with rough coefficients

Abstract

We derive local boundedness estimates for weak solutions of a large class of second-order quasilinear equations. The structural assumptions imposed on an equation in the class allow vanishing of the quadratic form associated with its principal part and require no smoothness of its coe cients. The class includes second-order linear elliptic equations as studied by Gilbarg-Trudinger (1998) and second-order subelliptic linear equations as studied by Sawyer-Wheeden (2006, 2010). Our results also extend ones obtained by J. Serrin (1964) concerning local boundedness of weak solutions of quasilinear elliptic equations