Extremal eigenvalues of measure differential equations with fixed variation  

作　　者：ZHANG MeiRong 1,2 1 Department of Mathematical Sciences,Tsinghua University,Beijing 100084,China 2 Zhou Pei-Yuan Center for Applied Mathematics,Tsinghua University,Beijing 100084,China 

出　　处：《Science China Mathematics》2010年第10期2573-2588,共16页中国科学：数学（英文版）

基　　金：supported by National Basic Research Program of China (Grant No.2006CB805903);National Natural Science Foundation of China (Grant No.10531010);Doctoral Fund of Ministry of Education of China (Grant No.20090002110079)

摘　　要：In this paper we will study eigenvalues of measure differential equations which are motivated by physical problems when physical quantities are not absolutely continuous.By taking Neumann eigenvalues of measure differential equations as an example,we will show how the extremal problems can be completely solved by exploiting the continuity results of eigenvalues in weak* topology of measures and the Lagrange multiplier rule for nonsmooth functionals.These results can give another explanation for extremal eigenvalues of SturmLiouville operators with integrable potentials.In this paper we will study eigenvalues of measure differential equations which are motivated by physical problems when physical quantities are not absolutely continuous.By taking Neumann eigenvalues of measure differential equations as an example,we will show how the extremal problems can be completely solved by exploiting the continuity results of eigenvalues in weak* topology of measures and the Lagrange multiplier rule for nonsmooth functionals.These results can give another explanation for extremal eigenvalues of SturmLiouville operators with integrable potentials.

关 键 词：MEASURE DIFFERENTIAL equation EIGENVALUE EXTREMAL value weak* topology Frechét derivative sub-differential 

分 类 号：O175.9[理学—数学]