Eigenfunctions of the Laplace operator and harmonic functions on model Riemannian manifolds

DOI10.1134/S1995080220110128zbMath1455.35159OpenAlexW3113394644WikidataQ115247363 ScholiaQ115247363MaRDI QIDQ828171

I. Romanova, Elena A. Mazepa, Alexander G. Losev

Publication date: 8 January 2021

Published in: Lobachevskii Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1995080220110128

zbMATH Keywords

Dirichlet problemasymptotic behavior of harmonic functionsmodel Riemannian manifold

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) General topics in linear spectral theory for PDEs (35P05) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Elliptic equations on manifolds, general theory (58J05) PDEs on manifolds (35R01)

Related Items (1)

Asymptotic behavior of solutions of the Dirichlet problem for the Poisson equation on model Riemannian manifolds

Cites Work

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• Concerning the \(L^ p\) norm of spectral clusters for second-order elliptic operators on compact manifolds
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• Solvability of the Dirichlet problem for the Poisson equation on some noncompact Riemannian manifolds
• Uniqueness of \({L}^{1}\) harmonic functions on rotationally symmetric Riemannian manifolds
• Bounds for eigenfunctions of the Laplacian on noncompact Riemannian manifolds
• UNIFORM BOUNDS FOR EIGENFUNCTIONS OF THE LAPLACIAN ON MANIFOLDS WITH BOUNDARY*
• Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds

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