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partial sum of eigenfunctions

ESAIM: Control, Optimisation and Calculus of Variations (1)

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

ESAIM: Control, Optimisation and Calculus of Variations / Volume 19 / Issue 1 / January 2013

Published online by Cambridge University Press:

11 May 2012, pp. 255-273

Print publication:

January 2013
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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.