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arXiv · 2506.02305

Characterization of positive superharmonic functions in a half-space

Lorenzo D'Ambrosio·Enzo Mitidieri
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Abstract

We prove a representation formula for superharmonic functions on the half-space $\mathbb{R}^N_+ := \mathbb{R}^{N-1}\times]0,+\infty[$. As a consequence, we derive some comparison principles and various positivity results.

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Lorenzo D'Ambrosio, Enzo Mitidieri. 2025-06-02. Characterization of positive superharmonic functions in a half-space. https://arxiv.org/abs/2506.02305

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