Harmonic Functions in a Cone Which Vanish on the Boundary

DOI10.1002/mana.19992020115zbMath0929.31001OpenAlexW2062335330MaRDI QIDQ4256170

Ikuko Miyamoto, Hidenobu Yoshida

Publication date: 23 September 1999

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.19992020115

zbMATH Keywords

Laplace operatorinfinite series representationeigenvalues in increasing order

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Series solutions to PDEs (35C10)

Related Items (5)

A priori bounds for semilinear equations and a new class of critical exponents for Lipschitz domains ⋮ Some properties for a subfunction associated with the stationary Schrödinger operator in a cone ⋮ On positive harmonic functions in cones and cylinders ⋮ Integral representations for harmonic functions of infinite order in a cone ⋮ Asymptotic behavior of positive harmonic functions in certain unbounded domains

Cites Work

• Solutions of the Dirichlet problem on a cone with continuous data
• Heat kernel estimates and lower bound of eigenvalues
• Harmonic majorization of a subharmonic function on a cone or on a cylinder
• The Generalized Ahlfors-Heins Theorem in Certain $d$-Dimensional Cones.
• Generalization of a theorem of Hayman on subharmonic functions in an 𝑚-dimensional cone
• Some Properties of the Eigenfunctions of The Laplace-Operator on Riemannian Manifolds

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