REGULARITY OF THE SOLUTIONS FOR NONLINEAR BIHARMONIC EQUATIONS IN |RN

doi:10.1016/S0252-9602(09)60119-3

数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (5): 1469-1480.doi: 10.1016/S0252-9602(09)60119-3

REGULARITY OF THE SOLUTIONS FOR NONLINEAR BIHARMONIC EQUATIONS IN |R^N

邓引斌, 李亦

Department of Mathematics, Huazhong |Normal University, |Wuhan 430079, China Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA and Department of Mathematics, Hunan Normal University, Changsha 410081, |China

收稿日期:2009-06-29 修回日期:2007-04-11 出版日期:2009-09-20 发布日期:2009-09-20
基金资助:
Research Supported by the National Natural Science Foundation of China (10631030), PHD specialized grant of Ministry of Education of China (20060511001) and supported in part by the Xiao-Xiang Special Fund, Hunan

REGULARITY OF THE SOLUTIONS FOR NONLINEAR BIHARMONIC EQUATIONS IN |R^N

DENG Yin-Bin, LI Yi

Department of Mathematics, Huazhong |Normal University, |Wuhan 430079, China Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA and Department of Mathematics, Hunan Normal University, Changsha 410081, |China

Received:2009-06-29 Revised:2007-04-11 Online:2009-09-20 Published:2009-09-20
Supported by:
Research Supported by the National Natural Science Foundation of China (10631030), PHD specialized grant of Ministry of Education of China (20060511001) and supported in part by the Xiao-Xiang Special Fund, Hunan

摘要/Abstract

摘要：

The purpose of this article is to establish the regularity of the weak solutions for the nonlinear biharmonic equation
{Δ²u+a(x)u=g(x, u),

u∈ H² (R^N), （1.1）

where the condition u ∈ H²(R^N) plays the role of a boundary value condition, and as well expresses explicitly that the differential equation is to be satisfied in the weak sense.

关键词: nonlinear biharmonic equation, regularity, fundamental solutions

Abstract:

The purpose of this article is to establish the regularity of the weak solutions for the nonlinear biharmonic equation
{Δ²u+a(x)u=g(x, u),

Key words: nonlinear biharmonic equation, regularity, fundamental solutions

中图分类号:

35B40

邓引斌, 李亦. REGULARITY OF THE SOLUTIONS FOR NONLINEAR BIHARMONIC EQUATIONS IN |R^N[J]. 数学物理学报(英文版), 2009, 29(5): 1469-1480.

DENG Yin-Bin, LI Yi. REGULARITY OF THE SOLUTIONS FOR NONLINEAR BIHARMONIC EQUATIONS IN |R^N[J]. Acta mathematica scientia,Series B, 2009, 29(5): 1469-1480.

参考文献

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REGULARITY OF THE SOLUTIONS FOR NONLINEAR BIHARMONIC EQUATIONS IN |R^N

REGULARITY OF THE SOLUTIONS FOR NONLINEAR BIHARMONIC EQUATIONS IN |R^N

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