Stationary p–harmonic maps approaching planar singular harmonic maps to the circle

期刊论文
发表日期：

2025年10月10日

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Marco Badran,
Jean Van Schaftingen

摘要

Given a bounded planar domain $\Omega \subset \mathbb {R}^2$ $Ω \subset R^{2}$ , we show that any singular harmonic map into the circle $\mathbb {S}^{1}$ $S^{1}$ corresponding to a topologically nondegenerate critical point of the renormalised energy in the sense of Bethuel, Brezis and Hélein is a limit of stationary p-harmonic maps for $p < 2$ $p < 2$ as $p \rightarrow 2$ $p \to 2$ .