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Boundary quasi-orthogonality and sharp inclusion bounds for large Dirichlet eigenvalues
[article]
2010
arXiv
pre-print
We study eigenfunctions and eigenvalues of the Dirichlet Laplacian on a bounded domain Ω⊂^n with piecewise smooth boundary. We bound the distance between an arbitrary parameter E > 0 and the spectrum {E_j } in terms of the boundary L^2-norm of a normalized trial solution u of the Helmholtz equation (Δ + E)u = 0. We also bound the L^2-norm of the error of this trial solution from an eigenfunction. Both of these results are sharp up to constants, hold for all E greater than a small constant, and
arXiv:1006.3592v1
fatcat:sykwejspvbgedjypyef2yejfhi