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

Published online by Cambridge University Press:  11 May 2012

Qi Lü
Qi Lü*
Affiliation:
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 610054, P.R. China. luqi59@163.com Basque Center for Applied Mathematics (BCAM), Mazarredo, 14, 48009 Bilbao Basque Country, Spain
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Abstract

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.

Keywords

Lower boundlocal energypartial sum of eigenfunctionsLaplace-Beltrami operatorRobin boundary condition
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 19 , Issue 1 , January 2013 , pp. 255 - 273
Copyright
© EDP Sciences, SMAI, 2012

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