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Pré-Publication, Document De Travail Année : 2024

Generic non-uniqueness of minimizing harmonic maps from a ball to a sphere

Résumé

In this note, we study non-uniqueness for minimizing harmonic maps from B3 to S2. We show that every boundary map can be modified to a boundary map that admits multiple minimizers of the Dirichlet energy by a small W1,p-change for p < 2. This strengthens a remark by the second-named author and Strzelecki. The main novel ingredient is a homotopy construction, which is the answer to an easier variant of a challenging question regarding the existence of a norm control for homotopies between W1,p maps.
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hal-04511102 , version 1 (19-03-2024)

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  • HAL Id : hal-04511102 , version 1

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Antoine Detaille, Katarzyna Mazowiecka. Generic non-uniqueness of minimizing harmonic maps from a ball to a sphere. 2024. ⟨hal-04511102⟩
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