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 differ...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.展开更多
By "an elementary configuration" we mean a set of a finite number of points,oriented byperplanes and oriented hyperspheres.In this paper,a complete solution of the following problems is given.Does there exis...By "an elementary configuration" we mean a set of a finite number of points,oriented byperplanes and oriented hyperspheres.In this paper,a complete solution of the following problems is given.Does there exist in Euclidean space a certain elementary configuration with a prescribed metric for cach pair of its elements? If so.how can one find the coordinate representations of the elements of such a configuration?展开更多
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)
文摘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.
基金Project supported by the National Natural Science Foundation of China
文摘By "an elementary configuration" we mean a set of a finite number of points,oriented byperplanes and oriented hyperspheres.In this paper,a complete solution of the following problems is given.Does there exist in Euclidean space a certain elementary configuration with a prescribed metric for cach pair of its elements? If so.how can one find the coordinate representations of the elements of such a configuration?
