Work

Poisson kernels on the half‐plane are bell‐shaped

Year: 2026

Type: article

Abstract: Consider a second‐order elliptic operator in the half‐plane with coefficients depending only on the second coordinate. The Poisson kernel for is used in the representation of positive ‐harmonic functions, that is, solutions of . In probabilistic terms, the Poisson kernel is the density function of the distribution of the diffusion in with generator at the hitting time of the boundary. We prove that the Poisson kernel for is bell‐shaped: its th derivative changes sign times. In particular, it is unimodal and it has two inflection points (it is concave, then convex and then concave again).

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70303

Author: Mateusz Kwaśnicki

Institution: Wrocław University of Science and Technology

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Narodowym Centrum Nauki

Award: G5142539128