Local behavior of solutions of quasi-linear equations

Abstract

This paper deals with the local behavior of solutions of quasi-linear partial differential equations of second order in n/> 2 independent variables. ~re shall be concerned specifically with the a priori majorization of solutions, the nature of removable singularities, and the behavior of a positive solution in the neighborhood of an isolated singularity. Corresponding results are for the most part well known for the case of the Laplace equation; roughly speaking, our work constitutes an extension of these results to a wide class of non-linear equations.