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.
Mots clés : lower bound, local energy, partial sum of eigenfunctions, Laplace-Beltrami operator, Robin boundary condition
@article{COCV_2013__19_1_255_0,
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},
pages = {255--273},
publisher = {EDP-Sciences},
volume = {19},
number = {1},
year = {2013},
doi = {10.1051/cocv/2012008},
mrnumber = {3023069},
zbl = {1258.93035},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2012008/}
}
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 SP - 255 EP - 273 VL - 19 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2012008/ DO - 10.1051/cocv/2012008 LA - en ID - COCV_2013__19_1_255_0 ER -
%0 Journal Article %A Lü, Qi %T A lower bound on local energy of partial sum of eigenfunctions for Laplace-Beltrami operators %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 255-273 %V 19 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2012008/ %R 10.1051/cocv/2012008 %G en %F COCV_2013__19_1_255_0
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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