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Applications p-harmoniques quand p tend vers 2

Van Vaerenbergh, BenoƮt
(2021)

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VanVaerenbergh_21251600_2021.pdf
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Details

Supervisors
Van Schaftingen, Jean
Faculty
FacultƩ des sciences
Degree label
Master [120] en sciences mathƩmatiques, Ơ finalitƩ approfondie
Abstract
enIn this master thesis, we study the asymptotic behavior of minimizers of the p-energy of Dirichlet, known as minimizing p-harmonic maps, when p tends to 2 by lower values. Minimizers map a regular and open set of the plane to a Riemannian manifold and their values are contrained on the boundary. Due to topological obstructions, existence of minimizers of the Dirichlet energy is not guaranteed. Convergence results of p-harmonic maps when p tends to 2 to renormalisable maps is established in various notions of convergence that we define. Our approach is based on an upper bound and a lower bound which we construct by means of an expansion of balls procedure. This process appeared first in the study of the Ginzburg-Landau functional. This method allows us to consider sequences of maps which are not necessary minimizers and not to rely on the regularity properties of p-harmonic maps.