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The Green's function of polyharmonic operators with diverging coefficients: Construction and sharp asymptotics

par Carletti, Lorenzo
Référence Journal of differential equations, 419, page (370-417)
Publication Publié, 2025-02-01

Article révisé par les pairs

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Résumé :

We show existence, uniqueness and positivity for the Green's function of the operator (Δg+α)k in a closed Riemannian manifold (M,g), of dimension n>2k, k∈N, k≥1, with Laplace-Beltrami operator Δg=−divg(∇⋅), and where α>0. We are interested in the case where α is large: We prove pointwise estimates with explicit dependence on α for the Green's function and its derivatives. We highlight a region of exponential decay for the Green's function away from the diagonal, for large α.