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

ESAIM: Control, Optimisation and Calculus of Variations (2013)

- Volume: 19, Issue: 1, page 255-273
- ISSN: 1292-8119

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topLü, Qi. "A lower bound on local energy of partial sum of eigenfunctions for Laplace-Beltrami operators." ESAIM: Control, Optimisation and Calculus of Variations 19.1 (2013): 255-273. <http://eudml.org/doc/272863>.

@article{Lü2013,

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.},

author = {Lü, Qi},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {lower bound; local energy; partial sum of eigenfunctions; Laplace-Beltrami operator; Robin boundary condition; Robin boundary conditions},

language = {eng},

number = {1},

pages = {255-273},

publisher = {EDP-Sciences},

title = {A lower bound on local energy of partial sum of eigenfunctions for Laplace-Beltrami operators},

url = {http://eudml.org/doc/272863},

volume = {19},

year = {2013},

}

TY - JOUR

AU - Lü, Qi

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

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2013

PB - EDP-Sciences

VL - 19

IS - 1

SP - 255

EP - 273

AB - 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.

LA - eng

KW - lower bound; local energy; partial sum of eigenfunctions; Laplace-Beltrami operator; Robin boundary condition; Robin boundary conditions

UR - http://eudml.org/doc/272863

ER -

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