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Pleijel’s theorem for a class of degenerate elliptic operators
Rupert L Frank, Bernard Helffer
Source abstract
Abstract We prove an asymptotic upper bound on the number of nodal domains of eigenfunctions of a class of degenerate elliptic operators. Our proof yields the same constant as in Pleijel’s bound for the Dirichlet Laplacian. The operators considered include the Baouendi–Grushin operator and operators with ellipticity degenerating on the boundary.
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