Gradient estimates and Liouville-type theorems for a weighted nonlinear elliptic equation

We consider gradient estimates for positive solutions to the following nonlinear elliptic equation on a smooth metric measure space [Formula: see text] : [Formula: see text] where a, b are two real constants. When the ∞-Bakry–Émery Ricci curvature is bounded from below, we obtain a global gradient e...

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Detalles Bibliográficos
Autores principales: Ma, Bingqing, Dong, Yongli
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5945720/
https://www.ncbi.nlm.nih.gov/pubmed/29773930
http://dx.doi.org/10.1186/s13660-018-1705-z
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author Ma, Bingqing
Dong, Yongli
author_facet Ma, Bingqing
Dong, Yongli
author_sort Ma, Bingqing
collection PubMed
description We consider gradient estimates for positive solutions to the following nonlinear elliptic equation on a smooth metric measure space [Formula: see text] : [Formula: see text] where a, b are two real constants. When the ∞-Bakry–Émery Ricci curvature is bounded from below, we obtain a global gradient estimate which is not dependent on [Formula: see text] . In particular, we find that any bounded positive solution of the above equation must be constant under some suitable assumptions.
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spelling pubmed-59457202018-05-15 Gradient estimates and Liouville-type theorems for a weighted nonlinear elliptic equation Ma, Bingqing Dong, Yongli J Inequal Appl Research We consider gradient estimates for positive solutions to the following nonlinear elliptic equation on a smooth metric measure space [Formula: see text] : [Formula: see text] where a, b are two real constants. When the ∞-Bakry–Émery Ricci curvature is bounded from below, we obtain a global gradient estimate which is not dependent on [Formula: see text] . In particular, we find that any bounded positive solution of the above equation must be constant under some suitable assumptions. Springer International Publishing 2018-05-10 2018 /pmc/articles/PMC5945720/ /pubmed/29773930 http://dx.doi.org/10.1186/s13660-018-1705-z Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Ma, Bingqing
Dong, Yongli
Gradient estimates and Liouville-type theorems for a weighted nonlinear elliptic equation
title Gradient estimates and Liouville-type theorems for a weighted nonlinear elliptic equation
title_full Gradient estimates and Liouville-type theorems for a weighted nonlinear elliptic equation
title_fullStr Gradient estimates and Liouville-type theorems for a weighted nonlinear elliptic equation
title_full_unstemmed Gradient estimates and Liouville-type theorems for a weighted nonlinear elliptic equation
title_short Gradient estimates and Liouville-type theorems for a weighted nonlinear elliptic equation
title_sort gradient estimates and liouville-type theorems for a weighted nonlinear elliptic equation
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5945720/
https://www.ncbi.nlm.nih.gov/pubmed/29773930
http://dx.doi.org/10.1186/s13660-018-1705-z
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