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 in terms of 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.
Boundedness of the weak solutions to quasilinear elliptic equations with Morrey data / Byun, S. S.; Palagachev, Dian Kostadinov. - In: INDIANA UNIVERSITY MATHEMATICS JOURNAL. - ISSN 0022-2518. - 62:5(2013), pp. 5115.1565-5115.1585. [10.1512/iumj.2013.62.5115]
Boundedness of the weak solutions to quasilinear elliptic equations with Morrey data
PALAGACHEV, Dian Kostadinov
2013-01-01
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 in terms of 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
