Optimal Potentials of Measure Differential Equations with Given Spectral Data

  • Zhiyuan WenEmail author
  • Lijuan Zhou
  • Meirong Zhang


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.


Measure differential equation Eigenvalue Potential Measure Spectral data 

Mathematics Subject Classification

34L15 34L40 58C07 



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. 1.School of Mathematical SciencesInner Mongolia UniversityHuhhotChina
  2. 2.Department of Mathematical SciencesTsinghua UniversityBeijingChina

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