A Pohozaev-type formula and Quantization of Horizontal Half-Harmonic Maps

2016/07/19 by Francesca Da Lio, Da Lio, Francesca, Paul Laurain +3
Mathematics · #34A08 #35B44 #35B65 #35J60 #58E20 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:34A08 #msc:35B44 #msc:35B65 #msc:35J60 #msc:58E20

paper · pdf · doi:10.48550/arxiv.1607.05504

41 pages

arxiv created 2016/07/19 · arxiv updated 2016/07/20

Abstract

In a recent paper the first and the third authors introduced the notion of horizontal α-harmonic map, with respect to a given C¹ planes distribution P_T on all R^m. The goal of this paper is to investigate compactness and quantization properties of sequences of horizontal 1/2- harmonic maps u_k in 1D. The quantization analysis is obtained through a precise asymptotic development of the energy of u_k in the neck regions and a subtle application of new Pohozaev-type formulae.

Related

• Horizontal α-Harmonic Maps
• Some Remarks on Pohozaev-Type Identities
• Compactness and Bubbles Analysis for 1/2-harmonic Maps
• On critical maps of the horizontal energy functional between Riemannian foliations
• A weak energy identity and the length of necks for a Sacks-Uhlenbeck α-harmonic map sequence