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On the Harnack inequality for quasilinear elliptic equations with a first-order term

Part of: Elliptic equations and systems Partial differential equations

Published online by Cambridge University Press:  22 February 2018

Susana Merchán ,
Luigi Montoro  and
Berardino Sciunzi
Susana Merchán
Affiliation:
Dipartimento di Matematica e Informatica, Universitá della Calabria, Ponte Pietro Bucci 31B, 87036 Arcavacata di Rende, Cosenza, Italy ([email protected]; [email protected]; [email protected])
Luigi Montoro
Affiliation:
Dipartimento di Matematica e Informatica, Universitá della Calabria, Ponte Pietro Bucci 31B, 87036 Arcavacata di Rende, Cosenza, Italy ([email protected]; [email protected]; [email protected])
Berardino Sciunzi
Affiliation:
Dipartimento di Matematica e Informatica, Universitá della Calabria, Ponte Pietro Bucci 31B, 87036 Arcavacata di Rende, Cosenza, Italy ([email protected]; [email protected]; [email protected])
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Abstract

We consider weak solutions to

with p > 1, q ≥ max{p − 1, 1}. We exploit the Moser iteration technique to prove a Harnack comparison inequality for C1 weak solutions. As a consequence we deduce a strong comparison principle.

Keywords

p-Laplace operatorHarnack inequalitycomparison principle

MSC classification

Primary: 35J92: Quasilinear elliptic equations with $p$-Laplacian 35B51: Comparison principles 35B06: Symmetries, invariants, etc.
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 5 , October 2018 , pp. 1075 - 1095
Copyright
Copyright © Royal Society of Edinburgh 2018 

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