Nonlinear elliptic equations with general growth in the gradient related to Gauss measure

Nonlinear elliptic equations with general growth in the gradient related to Gauss measure

In this article, we establish a comparison result through symmetrization for solutions to some problems with general growth in the gradient. This allows to get sharp estimates for the solutions, obtained by comparing them with solutions of simpler problems whose data depend only on the first var...

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Bibliographic Details
Main Authors: Yujuan Tian, Chao Ma, Fengquan Li
Format: Article
Language:English
Published: Texas State University 2015-12-01
Series:Electronic Journal of Differential Equations
Subjects:
Comparison results
symmetrization
gauss measure
nonlinear elliptic equation
Online Access:http://ejde.math.txstate.edu/Volumes/2015/305/abstr.html
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spelling doaj-4dac24c45dad402990ae1b73cd74762d2020-11-24T23:44:25ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912015-12-012015305,116Nonlinear elliptic equations with general growth in the gradient related to Gauss measureYujuan Tian0Chao Ma1Fengquan Li2 Shandong Normal Univ., Jinan, China Univ. of Jinan, Jinan, China Dalian Univ. of Technology, Dalian, China In this article, we establish a comparison result through symmetrization for solutions to some problems with general growth in the gradient. This allows to get sharp estimates for the solutions, obtained by comparing them with solutions of simpler problems whose data depend only on the first variable. Furthermore, we use such result to prove the existence of bounded solutions. All the above results are based on the study of a class of nonlinear integral operator of Volterra type.http://ejde.math.txstate.edu/Volumes/2015/305/abstr.htmlComparison resultssymmetrizationgauss measurenonlinear elliptic equation
collection DOAJ
language English
format Article
sources DOAJ
author Yujuan Tian
Chao Ma
Fengquan Li
spellingShingle Yujuan Tian
Chao Ma
Fengquan Li
Nonlinear elliptic equations with general growth in the gradient related to Gauss measure
Electronic Journal of Differential Equations
Comparison results
symmetrization
gauss measure
nonlinear elliptic equation
author_facet Yujuan Tian
Chao Ma
Fengquan Li
author_sort Yujuan Tian
title Nonlinear elliptic equations with general growth in the gradient related to Gauss measure
title_short Nonlinear elliptic equations with general growth in the gradient related to Gauss measure
title_full Nonlinear elliptic equations with general growth in the gradient related to Gauss measure
title_fullStr Nonlinear elliptic equations with general growth in the gradient related to Gauss measure
title_full_unstemmed Nonlinear elliptic equations with general growth in the gradient related to Gauss measure
title_sort nonlinear elliptic equations with general growth in the gradient related to gauss measure
publisher Texas State University
series Electronic Journal of Differential Equations
issn 1072-6691
publishDate 2015-12-01
description In this article, we establish a comparison result through symmetrization for solutions to some problems with general growth in the gradient. This allows to get sharp estimates for the solutions, obtained by comparing them with solutions of simpler problems whose data depend only on the first variable. Furthermore, we use such result to prove the existence of bounded solutions. All the above results are based on the study of a class of nonlinear integral operator of Volterra type.
topic Comparison results
symmetrization
gauss measure
nonlinear elliptic equation
url http://ejde.math.txstate.edu/Volumes/2015/305/abstr.html
work_keys_str_mv AT yujuantian nonlinearellipticequationswithgeneralgrowthinthegradientrelatedtogaussmeasure
AT chaoma nonlinearellipticequationswithgeneralgrowthinthegradientrelatedtogaussmeasure
AT fengquanli nonlinearellipticequationswithgeneralgrowthinthegradientrelatedtogaussmeasure
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