Gradient estimates and comparison principlefor some nonlinear elliptic equations

Maria Francesca Betta; Rosaria Di Nardo; Anna Mercaldo; Adamaria Perrotta

doi:10.3934/cpaa.2015.14.897

Article Contents

2015, Volume 14, Issue 3: 897-922. Doi: 10.3934/cpaa.2015.14.897

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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
2.
Università degli Studi di Napoli Federico II, Dipartimento di Matematica e Applicazioni "R. Caccioppoli", Complesso Monte S. Angelo, Via Cintia, 80126 Napoli
3.
Dipartimento di Matematica e Applicazioni "R. Caccioppoli", Universitá di Napoli "Federico II", via Cintia, I-80126 Napoli

Received: June 30, 2014

Revised: December 31, 2014

Published: April 2015

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Abstract

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.

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Mathematics Subject Classification: Primary: 35J25; Secondary: 35J60.

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References

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