关于Pucci算子的抛物方程的Liouville定理

doi:10.3969/j.issn.1007-2985.2013.01.003

journal6 ›› 2013, Vol. 34 ›› Issue (1): 11-13.DOI: 10.3969/j.issn.1007-2985.2013.01.003

关于Pucci算子的抛物方程的Liouville定理

(华北电力大学数理学院，北京102206)

出版日期:2013-01-25 发布日期:2013-01-22

Liouville Type Theorem for a Parabolic Equation Involving Pucci Operato

(Department of Mathematics and Physics,North China Electric Power University,Beijing 102206,China)

Online:2013-01-25 Published:2013-01-22
About author:LIU Yong (1980-),male,was born in Jiangying,Jiangsu Province,lecturer;main research areas are nonlinear analysis and nonlinear partial differential equations.
Supported by:
National Natural Science Foundation of China (11101141);Scientific Research Foundation for the Returned Overseas Chinese Scholars of the State Education Ministry;Doctoral Funding of North China Electric Power University

摘要/Abstract

摘要：关于含有Laplace算子的超线性抛物方程的一个经典结果是Liouville型的定理.由于这些定理在应用中的重要性，研究了关于Pucci算子的抛物方程的Liouville型定理.在空间变量为1维的情形下，Pucci算子的性质相对容易分析，对这一特殊情形，证明了对应的抛物方程没有全局有界的正解.

关键词： Pucci算子, 全局解, Liouville型定理

Abstract: One classical result for the superlinear parabolic equation involving Laplacian operator is the Liouville type theorem.Due to the importance of these kind of theorems,the Liouville type theorem for parabolic equation involving Pucci’s operator is studied in this paper.When the space variable is one dimensional,it is relatively easy to analyze the Pucci operator.The main result of this paper states that in this case,the corresponding equation does not have global positive bounded solution.

Key words: Pucci operator, global solution, Liouville type theorem

刘勇. 关于Pucci算子的抛物方程的Liouville定理[J]. journal6, 2013, 34(1): 11-13.

LIU Yong. Liouville Type Theorem for a Parabolic Equation Involving Pucci Operato[J]. journal6, 2013, 34(1): 11-13.

关于Pucci算子的抛物方程的Liouville定理

Liouville Type Theorem for a Parabolic Equation Involving Pucci Operato

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