Hyperbolic Laplace operator and the Weinstein equation in \(\mathbb R^3\)

DOI10.1007/s00006-013-0425-1zbMath1297.35252OpenAlexW2013345043MaRDI QIDQ742324

Sirkka-Liisa Eriksson, Heikki Orelma

Publication date: 18 September 2014

Published in: Advances in Applied Clifford Algebras (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00006-013-0425-1

zbMATH Keywords

Laplace-Beltrami operatorWeinstein equationBrelot harmonic spaceshyperbolic Laplace operatorPoincaré upper half space

Mathematics Subject Classification ID

Second-order hyperbolic equations (35L10) PDEs on manifolds (35R01)

Related Items (7)

Homogeneous \((\alpha,k)\)-polynomial solutions of the fractional Riesz system in hyperbolic space ⋮ Lie symmetries of fundamental solutions to the Leutwiler-Weinstein equation ⋮ Fundamental solutions for the Laplace-Beltrami operator defined by the conformal hyperbolic metric and Jacobi polynomials ⋮ On the solution of a Weinstein-type equation in \(\mathbb{R}^3\) ⋮ A New Cauchy Type Integral Formula for Quaternionic k-hypermonogenic Functions ⋮ Electrostatic fields in some special inhomogeneous media and new generalizations of the Cauchy-Riemann system ⋮ \((m,h)\)-monogenic functions related to axially symmetric Helmholtz equations

Cites Work

• Mean value properties for the Weinstein equation using the hyperbolic metric
• Hyperbolic extensions of integral formulas
• Best constants in the Harnack inequality for the Weinstein equation
• On the uniqueness of generalized axially symmetric potentials
• A mean-value theorem for some eigenfunctions of the Laplace-Beltrami operator on the upper-half space
• A Hyperbolic Interpretation of Cauchy-Type Kernels in Hyperbolic Function Theory
• Generalized axially symmetric potential theory
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