Asymptotic behavior of minimizing p-harmonic maps when p↗2 in dimension 2
(2023) Calculus of Variations and Partial Differential Equations — Vol. 62, n° 8, p. 229 (2023)
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- Abstract
- We study p-harmonic maps with Dirichlet boundary conditions from a planar domain into a general compact Riemannian manifold. We show that as p approaches 2 from below, they converge up to a subsequence to a minimizing singular renormalizable harmonic map. The singularities are imposed by topological obstructions to the existence of harmonic mappings; the location of the singularities being governed by a renormalized energy. Our analysis is based on lower bounds on growing balls and also yields some uniform weak-Lp bounds (also known as Marcinkiewicz or Lorentz Lp,∞).
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Van Schaftingen, J., & Van Vaerenbergh, B. (2023). Asymptotic behavior of minimizing p-harmonic maps when p↗2 in dimension 2. Calculus of Variations and Partial Differential Equations, 62(8), 229. https://doi.org/10.1007/s00526-023-02568-6 (Original work published 2023)