The viscosity solutions of a nonlinear equation related to the <em>p-Laplacian</em>

The viscosity solutions of a nonlinear equation related to the <em>p-Laplacian</em>

The viscosity solutions of a nonlinear equation related to the <em>p-Laplacian</em> are considered. Besides there is a damping term in the equation, a nonlocal function is added. By considering the regularized problem and using Moser iteration technique, we get the uniformly local bounde...

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Main Authors: Qitong Ou, Huashui Zhan
Format: Article
Language:English
Published: AIMS Press 2017-06-01
Series:AIMS Mathematics
Subjects:
Nonlinear equation| <em>p-Laplacian</em>| moser iteration| viscosity solution
Online Access:http://www.aimspress.com/article/10.3934/Math.2017.3.400/fulltext.html
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spelling doaj-2ab2727b8e2e47fe9dcc730e23614f4a2020-11-25T01:43:57ZengAIMS PressAIMS Mathematics2473-69882017-06-012340042110.3934/Math.2017.3.400The viscosity solutions of a nonlinear equation related to the <em>p-Laplacian</em>Qitong Ou0Huashui Zhan1School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, P. R. ChinaSchool of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, P. R. ChinaThe viscosity solutions of a nonlinear equation related to the <em>p-Laplacian</em> are considered. Besides there is a damping term in the equation, a nonlocal function is added. By considering the regularized problem and using Moser iteration technique, we get the uniformly local bounded properties of the solutions and the <em>L<sup>p</sup></em>-norm for the gradients. By the compactness theorem, we prove the existence of the viscosity solution of the equation.http://www.aimspress.com/article/10.3934/Math.2017.3.400/fulltext.htmlNonlinear equation| <em>p-Laplacian</em>| moser iteration| viscosity solution
collection DOAJ
language English
format Article
sources DOAJ
author Qitong Ou
Huashui Zhan
spellingShingle Qitong Ou
Huashui Zhan
The viscosity solutions of a nonlinear equation related to the <em>p-Laplacian</em>
AIMS Mathematics
Nonlinear equation| <em>p-Laplacian</em>| moser iteration| viscosity solution
author_facet Qitong Ou
Huashui Zhan
author_sort Qitong Ou
title The viscosity solutions of a nonlinear equation related to the <em>p-Laplacian</em>
title_short The viscosity solutions of a nonlinear equation related to the <em>p-Laplacian</em>
title_full The viscosity solutions of a nonlinear equation related to the <em>p-Laplacian</em>
title_fullStr The viscosity solutions of a nonlinear equation related to the <em>p-Laplacian</em>
title_full_unstemmed The viscosity solutions of a nonlinear equation related to the <em>p-Laplacian</em>
title_sort viscosity solutions of a nonlinear equation related to the <em>p-laplacian</em>
publisher AIMS Press
series AIMS Mathematics
issn 2473-6988
publishDate 2017-06-01
description The viscosity solutions of a nonlinear equation related to the <em>p-Laplacian</em> are considered. Besides there is a damping term in the equation, a nonlocal function is added. By considering the regularized problem and using Moser iteration technique, we get the uniformly local bounded properties of the solutions and the <em>L<sup>p</sup></em>-norm for the gradients. By the compactness theorem, we prove the existence of the viscosity solution of the equation.
topic Nonlinear equation| <em>p-Laplacian</em>| moser iteration| viscosity solution
url http://www.aimspress.com/article/10.3934/Math.2017.3.400/fulltext.html
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AT qitongou viscositysolutionsofanonlinearequationrelatedtotheemplaplacianem
AT huashuizhan viscositysolutionsofanonlinearequationrelatedtotheemplaplacianem
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