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

Abstract

In a recent paper the first and the third authors introduced the notion of horizontal α-harmonic map, with respect to a given C^1 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.

41 pages

References in corpus (2)

• Sub-criticality of non-local Schrödinger systems with antisymmetric potentials and applications to half-harmonic maps
• 3-Commutators Estimates and the Regularity of 1/2 Harmonic Maps into Spheres

Cited by in corpus (2)

• On regularity theory for n/p-harmonic maps into manifolds
• Existence, Uniqueness and Regularity of the Fractional Harmonic Gradient Flow in General Target Manifolds