Title: Regularity of weak solutions of homogeneous or inhomogeneous quasilinear elliptic equations

Authors: Patrizia Pucci and Raffaella Servadei

Issue: Volume 57 (2008), Issue 7, 3329-3364

Abstract: In this paper we give several regularity results for weak solutions of quasilinear elliptic equations, of homogeneous or inhomogeneous type, by using the Moser iteration scheme and the translation method due to Nirenberg under suitable growth conditions on the nonlinear term. The theorems established generalize some results already appeared in literature. Also radial weak solutions of the problem are considered and, in this case, further properties, which find a first application in [P. Pucci and R. Servadei, \emph{Existence, non-existence and regularity of radial ground states for $p$-Laplacian equations with singular weights}, Ann. Inst. H. Poincar\'e A.N.L. \textbf{25} (2008), 505--537], are proved.