American Institute of Mathematical Sciences

May  2015, 14(3): 897-922. doi: 10.3934/cpaa.2015.14.897

Gradient estimates and comparison principle for some nonlinear elliptic equations

 1 Università degli Studi di Napoli "Parthenope", Dipartimento di Ingegneria, Centro Direzionale, Isola C4 80143 Napoli, Italy 2 Università degli Studi di Napoli Federico II, Dipartimento di Matematica e Applicazioni "R. Caccioppoli", Complesso Monte S. Angelo, Via Cintia, 80126 Napoli, Italy, Italy 3 Dipartimento di Matematica e Applicazioni "R. Caccioppoli", Universitá di Napoli "Federico II", via Cintia, I-80126 Napoli

Received  July 2014 Revised  January 2015 Published  March 2015

We consider a class of Dirichlet boundary problems for nonlinear elliptic equations with a first order term. We show how the summability of the gradient of a solution increases when the summability of the datum increases. We also prove comparison principle which gives in turn uniqueness results by strenghtening the assumptions on the operators.
Citation: Maria Francesca Betta, Rosaria Di Nardo, Anna Mercaldo, Adamaria Perrotta. Gradient estimates and comparison principle for some nonlinear elliptic equations. Communications on Pure & Applied Analysis, 2015, 14 (3) : 897-922. doi: 10.3934/cpaa.2015.14.897
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