Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-26T16:01:58.957Z Has data issue: false hasContentIssue false
  • English
  • Français

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])
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)