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Extremal eigenvalues of measure differential equations with fixed variation

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Abstract

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 Sturm-Liouville operators with integrable potentials.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    MeiRong Zhang

  2. Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing, 100084, China

    MeiRong Zhang

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  1. MeiRong Zhang
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Correspondence to MeiRong Zhang.

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Zhang, M. Extremal eigenvalues of measure differential equations with fixed variation. Sci. China Math. 53, 2573–2588 (2010). https://doi.org/10.1007/s11425-010-4081-9

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  • DOI: https://doi.org/10.1007/s11425-010-4081-9

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