Mean value properties for the Weinstein equation using the hyperbolic metric

DOI10.1007/s11785-012-0280-4zbMath1275.30011OpenAlexW1990609514MaRDI QIDQ371899

Heikki Orelma, Sirkka-Liisa Eriksson

Publication date: 10 October 2013

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11785-012-0280-4

zbMATH Keywords

harmonic functionLaplace-Beltrami operatorhyperbolic metricconformal manifoldWeinstein equation

Mathematics Subject Classification ID

Conformal metrics (hyperbolic, Poincaré, distance functions) (30F45)

Related Items (10)

Vekua systems in hyperbolic harmonic analysis ⋮ On \(k\)-hypermonogenic functions and their mean value properties ⋮ On Orthonormal harmonic polynomials ⋮ Solutions of Weinstein type equations, Carleson measures and \(\mathrm{BMO}(\mathbb{R}_+, dm_\lambda)\) ⋮ Contributions to modified spherical harmonics in four dimensions ⋮ A New Cauchy Type Integral Formula for Quaternionic k-hypermonogenic Functions ⋮ Hyperbolic function theory in the skew-field of quaternions ⋮ On Vekua systems and their connections to hyperbolic function theory in the plane ⋮ Hyperbolic Laplace operator and the Weinstein equation in \(\mathbb R^3\) ⋮ Solutions of Weinstein equations representable by Bessel Poisson integrals of BMO functions

Cites Work

• Best constants in the Harnack inequality for the Weinstein equation
• A Hyperbolic Interpretation of Cauchy-Type Kernels in Hyperbolic Function Theory
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