A lower bound on local energy of partial sum of eigenfunctions for Laplace-Beltrami operators
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 255-273.

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.

DOI : https://doi.org/10.1051/cocv/2012008
Classification : 93B07
Mots clés : lower bound, local energy, partial sum of eigenfunctions, Laplace-Beltrami operator, Robin boundary condition
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author = {L\"u, Qi},
title = {A lower bound on local energy of partial sum of eigenfunctions for {Laplace-Beltrami} operators},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
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Lü, Qi. A lower bound on local energy of partial sum of eigenfunctions for Laplace-Beltrami operators. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 255-273. doi : 10.1051/cocv/2012008. http://www.numdam.org/articles/10.1051/cocv/2012008/

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