Isoperimetric Upper Bounds and Reilly-Type Inequalities for the First Eigenvalue of the $p$-Biharmonic Operator
Received:October 31, 2022  Revised:January 08, 2023
Key Words: eigenvalue   $p$-biharmonic operator   isoperimetric upper bounds   Reilly-type inequalities  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.12071051).
Author NameAffiliation
Xuesen QI School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
Yunguang YUE School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
Ximin LIU School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
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Abstract:
      In this paper, we give some isoperimetric upper bounds for the first eigenvalue of the $p$-biharmonic operator of an $n$-dimensional embedded closed hypersurface in an Euclidean space. We also give Reilly-type inequalities for the first eigenvalue of the $p$-biharmonic operator of an $n$-dimensional closed submanifold immersed into a higher dimensional manifold such as an Euclidean space, a unit sphere, a projective space.
Citation:
DOI:10.3770/j.issn:2095-2651.2023.04.011
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