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

Published online by Cambridge University Press:  22 February 2018

Susana Merchán
Affiliation:
Dipartimento di Matematica e Informatica, Universitá della Calabria, Ponte Pietro Bucci 31B, 87036 Arcavacata di Rende, Cosenza, Italy (merchan@mat.unical.it; montoro@mat.unical.it; sciunzi@mat.unical.it)
Luigi Montoro
Affiliation:
Dipartimento di Matematica e Informatica, Universitá della Calabria, Ponte Pietro Bucci 31B, 87036 Arcavacata di Rende, Cosenza, Italy (merchan@mat.unical.it; montoro@mat.unical.it; sciunzi@mat.unical.it)
Berardino Sciunzi
Affiliation:
Dipartimento di Matematica e Informatica, Universitá della Calabria, Ponte Pietro Bucci 31B, 87036 Arcavacata di Rende, Cosenza, Italy (merchan@mat.unical.it; montoro@mat.unical.it; sciunzi@mat.unical.it)
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Abstract

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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.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2018