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Optimal Potentials of Measure Differential Equations with Given Spectral Data

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Abstract

In this paper, we consider the Dirichlet eigenvalue problems of second-order measure differential equations with a general distribution of potentials. The following optimization problem will be solved: when the m-th eigenvalue is known, we will find explicitly what distribution of potentials will have the minimal total variation. The main tool used herein is some deep continuity results on eigenvalues.

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Acknowledgements

The first two authors are supported by the Scientific Starting Research Foundation of Inner Mongolia University (No. 21200-5175108 and No. 20100-5165106). The third author is supported by the National Natural Science Foundation of China (Grant No. 11790273).

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Authors and Affiliations

  1. School of Mathematical Sciences, Inner Mongolia University, Huhhot, 010021, China

    Zhiyuan Wen & Lijuan Zhou

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

    Meirong Zhang

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  1. Zhiyuan Wen
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  2. Lijuan Zhou
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  3. Meirong Zhang
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Correspondence to Zhiyuan Wen.

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Communicated by Paolo Maria Mariano.

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Wen, Z., Zhou, L. & Zhang, M. Optimal Potentials of Measure Differential Equations with Given Spectral Data. J Optim Theory Appl 184, 139–161 (2020). https://doi.org/10.1007/s10957-018-01462-y

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