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- W3174592428 abstract "We study the sharp doubling inequalities for the gradients and upper bounds for the critical sets of Dirichlet eigenfunctions on the boundary and in the interior of compact Riemannian manifolds. Most efforts are devoted to obtaining the sharp doubling inequalities for the gradients. New idea is developed to overcome the difficulties on the unavailability of the double manifold in obtaining doubling inequalities in smooth manifolds. The sharp upper bounds of critical sets in analytic Riemannian manifolds are consequences of the doubling inequalities." @default.
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- W3174592428 date "2021-10-01" @default.
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- W3174592428 title "Doubling inequalities and critical sets of Dirichlet eigenfunctions" @default.
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- W3174592428 doi "https://doi.org/10.1016/j.jfa.2021.109155" @default.
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