Liouville-type theorems and decay estimates for solutions to higher order elliptic equations
Liouville-type theorems and decay estimates for solutions to higher order elliptic equations
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DOI：
10.1016/j.anihpc.2012.02.004
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发表时间：
2012-09
影响因子：
1.9
通讯作者：
G. Lu;Peiyong Wang;Jiuyi Zhu
中科院分区：
文献类型：
--
作者：
G. Lu;Peiyong Wang;Jiuyi Zhu
Liouville型定理是求解偏微分方程的有力工具。解的有界性假设经常被强加在导出这样的刘维尔型定理。本文对某些类型的椭圆型方程和方程组，在不作非负解有界性假设的情况下，建立了几个Liouville型定理。使用重新缩放技术和加倍引理最近在Polácik等人。（2007）[20]，我们改进了高阶椭圆型方程、半线性方程和椭圆型方程组中的几个Liouville型定理.更具体地说，我们删除了有界性假设的解决方案，这是需要在相应的刘维尔型定理在最近的文献中的证明。此外，我们还研究了高阶椭圆型方程的奇异性和衰减估计。All rights reserved.
Liouville-type theorems are powerful tools in partial differential equations. Boundedness assumptions of solutions are often imposed in deriving such Liouville-type theorems. In this paper, we establish some Liouville-type theorems without the boundedness assumption of nonnegative solutions to certain classes of elliptic equations and systems. Using a rescaling technique and doubling lemma developed recently in Polácik et al.(2007)[20], we improve several Liouville-type theorems in higher order elliptic equations, some semilinear equations and elliptic systems. More specifically, we remove the boundedness assumption of the solutions which is required in the proofs of the corresponding Liouville-type theorems in the recent literature. Moreover, we also investigate the singularity and decay estimates of higher order elliptic equations.© 2012 Elsevier Masson SAS. All rights reserved.