Positive Harmonic Functions Vanishing on the Boundary for the Laplacian in Unbounded Horn-Shaped Domains

DOI10.2307/2154652zbMath0807.31001OpenAlexW4244523487MaRDI QIDQ4292728

Ross G. Pinsky, Dimitry Ioffe

Publication date: 26 February 1995

Full work available at URL: https://doi.org/10.2307/2154652

zbMATH Keywords

harmonic functionsdiffusion processesMartin boundary at infinity

Mathematics Subject Classification ID

Brownian motion (60J65) Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Martin boundary theory (31C35) Second-order elliptic equations (35J15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (4)

A probabilistic approach to positive harmonic functions in a slab with alternating Dirichlet and Neumann boundary conditions ⋮ Generalized Cranston-McConnell inequalities and Martin boundaries of unbounded domains ⋮ Ratio limit theorem for parabolic horn-shaped domains ⋮ Martin boundaries of elliptic skew products, semismall perturbations, and fundamental solutions of parabolic equations

Cites Work

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• On the Martin boundary of Lipschitz strips
• A probabilistic approach to a theorem of Gilbarg and Serrin
• Principle de Harnack à la frontière et théorème de Fatou pour un opérateur elliptique dans un domaine lipschitzien
• A new approach to the Martin boundary via diffusions conditioned to hit a compact set
• Conditional brownian motion and the boundary limits of harmonic functions
• Positive Harmonic Functions on Lipschitz Domains

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