Asymptotic behavior of minimizing $p$-harmonic maps when $p \nearrow 2$ in dimension 2
| Autor: | Van Schaftingen, Jean, Van Vaerenbergh, Benoît |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00526-023-02568-6 |
| Popis: | 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-$L^p$ bounds (also known as Marcinkiewicz or Lorentz $L^{p,\infty}$). Comment: 40 pages, typographical corrections |
| Databáze: | arXiv |
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