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

Badran, Marco;Van Schaftingen, Jean
(2025) Calculus of Variations and Partial Differential Equations — Vol. 64, n° 282 (2025)

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Abstract
Given a bounded planar domain Ω of ℝ², we show that any singular harmonic map into the circle S¹ 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 as p→2.
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Badran, M., & Van Schaftingen, J. (2025). Stationary p–harmonic maps approaching planar singular harmonic maps to the circle. Calculus of Variations and Partial Differential Equations, 64(282). https://doi.org/10.1007/s00526-025-03160-w (Original work published 2025)