DOAJ Open Access 2024

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

Detaille, Antoine Mazowiecka, Katarzyna

Abstrak

In this note, we study non-uniqueness for minimizing harmonic maps from $B^3$ to $§^2$. We show that every boundary map can be modified to a boundary map that admits multiple minimizers of the Dirichlet energy by a small $W^{1,p}$-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 $ W^{1,p} $ maps.

Topik & Kata Kunci

Mathematics

Penulis (2)

Detaille, Antoine

Mazowiecka, Katarzyna

Format Sitasi

APA MLA BibTeX

Antoine, D., Katarzyna, M. (2024). Generic non-uniqueness of minimizing harmonic maps from a ball to a sphere. https://doi.org/10.5802/crmath.648

Akses Cepat

PDF tidak tersedia langsung

Cek di sumber asli →

Lihat di Sumber doi.org/10.5802/crmath.648

Informasi Jurnal

Tahun Terbit: 2024
Sumber Database: DOAJ
DOI: 10.5802/crmath.648
Akses: Open Access ✓