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arXiv · 2510.15249

The Wiener Criterion at $\infty$ for Degenerate Elliptic Equations

Ugur G. Abdulla·Denis Brazke
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Abstract

This paper establishes a Wiener criterion at $\infty$ to characterise the unique solvability of the Dirichlet problem for degenerate elliptic equations with power-like weights in arbitrary open sets. In the measure-theoretical context, the criterion determines whether the $\A$-harmonic measure of $\infty$ is null or positive. From the topological point of view, it presents a test for the thinness of the exterior set at $\infty$ in the $\A$-fine topology.

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Ugur G. Abdulla, Denis Brazke. 2025-10-17. The Wiener Criterion at $\infty$ for Degenerate Elliptic Equations. https://arxiv.org/abs/2510.15249

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