Generalized Cranston-McConnell inequalities and Martin boundaries of unbounded domains

DOI10.1007/BF02787105zbMath0865.31009OpenAlexW1968503052MaRDI QIDQ2565377

Minoru Murata, Hiroaki Aikawa

Publication date: 8 July 1997

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02787105

zbMATH Keywords

bounded and unbounded domainsMartin boundaryexamplesMartin compactificationinequality of Cranston and McConnell

Mathematics Subject Classification ID

Martin boundary theory (31C35) Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (9)

Positive solutions of Schrödinger equations in product form and Martin compactifications of the plane ⋮ Semismall perturbations, semi-intrinsic ultracontractivity, and integral representations of nonnegative solutions for parabolic equations ⋮ Unnamed Item ⋮ Semismall perturbations in the Martin theory for elliptic equations ⋮ Integral representations of nonnegative solutions for parabolic equations and elliptic Martin boundaries ⋮ Positive solutions of Schrödinger equations in product form and Martin compactifications of the plane. II ⋮ Sharp estimates for the Green function, 3G inequalities, and nonlinear Schrödinger problems in uniform cones ⋮ Potential theoretic notions related to integrability of superharmonic functions and supertemperatures ⋮ Martin boundaries of elliptic skew products, semismall perturbations, and fundamental solutions of parabolic equations

Cites Work

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• On construction of Martin boundaries for second order elliptic equations
• The lifetime of conditional Brownian motion in the plane
• On an estimate of Cranston and McConnell for elliptic diffusions in uniform domains
• Structure of positive solutions to \((-\Delta +V)u=0\) in \(R^ n\)
• On the Martin boundary of Lipschitz strips
• On positive solutions of second-order elliptic equations, stability results, and classification
• On the upper bounds of Green potentials
• Positive Harmonic Functions Vanishing on the Boundary for the Laplacian in Unbounded Horn-Shaped Domains
• The lifetime of conditioned Brownian motion
• Minimal Positive Harmonic Functions

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