IUMJ

Title: Boundedness of the weak solutions to quasilinear elliptic equations with Morrey data

Authors: Sun-Sig Byun and Dian Palagachev

Issue: Volume 62 (2013), Issue 5, 1565-1585

Abstract:

We prove global essential boundedness of weak solutions to quasilinear coercive divergence form equations with data belonging to Morrey spaces. The nonlinear terms are given by Carath\'eodory functions and satisfy controlled growth assumptions. As an application of the main result, we get global H\"older continuity of the solutions to semilinear elliptic equations with measurable coefficients and Morrey data.