Research-Asymptotic Behavior of Harmonic Functions on Irregular Domains

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Asymptotic Behavior of Harmonic Functions on Irregular Domains

Speaker: Zongyuan Li（City University of Hong Kong）
Time: Nov 17, 2026, 14:00-15:00
Location: Room M616, College of Science Building

Abstract

This talk explores the asymptotic properties of harmonic functions near conical boundary points, addressing three primary questions: the conditions under which harmonic functions are asymptotically homogeneous, the uniqueness of Almgren blow-up limits, and the existence of asymptotic expansions. Unlike previous studies focused on domains with at least $C^{1,Dini}$ smoothness, this work considers domains meeting specific one-point conditions where traditional Almgren-type monotonicity formulas do not apply. To address these challenges, we introduce a compactness method as an alternative tool. This is joint work with Dennis Kriventsov (Rutgers).