A lower bound on local energy of partial sum of eigenfunctions for Laplace-Beltrami operators

In this paper, a lower bound is established for the local energy of partial sum of eigenfunctions for Laplace-Beltrami operators (in Riemannian manifolds with low regularity data) with general boundary condition. This result is a consequence of a new pointwise and weighted estimate for Laplace-Beltr...

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Bibliographic Details
Published inESAIM. Control, optimisation and calculus of variations Vol. 19; no. 1; pp. 255 - 273
Main Author Lü, Qi
Format Journal Article
LanguageEnglish
Published Les Ulis EDP Sciences 01.01.2013
Subjects
93B07
Boundary conditions
Calculus of variations
Control theory
Energy
Inequality
Laplace transforms
Laplace-Beltrami operator
local energy
Lower bound
Mathematical models
Mathematics
partial sum of eigenfunctions
Robin boundary condition
Studies
Topological manifolds
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Summary:In this paper, a lower bound is established for the local energy of partial sum of eigenfunctions for Laplace-Beltrami operators (in Riemannian manifolds with low regularity data) with general boundary condition. This result is a consequence of a new pointwise and weighted estimate for Laplace-Beltrami operators, a construction of some nonnegative function with arbitrary given critical point location in the manifold, and also two interpolation results for solutions of elliptic equations with lateral Robin boundary conditions.
Bibliography:PII:S1292811912000085
This work is partially supported by the NSF of China under Grants 10831007, 11101070 and 60974035. This paper is an improved version of one chapter of the author’s Ph.D. thesis [13] accomplished at Sichuan University under the guidance of Professor Xu Zhang. The author would like to take this opportunity to thank him deeply for his help.
luqi59@163.com
ark:/67375/80W-JH9M6F8C-R
istex:9C318FCFADA70F452EF916AE5A2E48B7B9298371
publisher-ID:cocv120008
ISSN:1292-8119
1262-3377
DOI:10.1051/cocv/2012008