Propri\'et\'e de convergence de certaines familles de fonctions finement harmoniques et r\'egularit\'e du noyau de Green d'un domaine fin

TL;DR

This paper establishes a convergence property for certain families of finely harmonic functions on fine domains in ^n and uses it to demonstrate regularity of the fine Green kernel, advancing potential theory.

Contribution

It introduces a new convergence property for finely harmonic functions and applies it to prove regularity of the Green kernel in fine potential theory.

Findings

Proves a convergence property for families of finely harmonic functions.

Establishes regularity results for the fine Green kernel.

Enhances understanding of fine potential theory in ^n.

Abstract

We prove a convergence property for some families of finely harmonic functions on a fine domain $U$ of $\RR^n$ ($n\ge 2$), and we apply it to prove some regularity of the fine Green kernel of $U$.