Geodesic
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 Cet article a éte moissonné depuis la source Numdam

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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 : 10.1051/cocv/2012008
Classification : 93B07
Keywords: 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},
     pages = {255--273},
     year = {2013},
     publisher = {EDP-Sciences},
     volume = {19},
     number = {1},
     doi = {10.1051/cocv/2012008},
     mrnumber = {3023069},
     zbl = {1258.93035},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2012008/}
}
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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

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