Compactness and bubble analysis for -harmonic maps

  • Francesca Da Lio

    Department of Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland

Abstract

In this paper we study compactness and quantization properties of sequences of -harmonic maps such that . More precisely we show that there exist a weak -harmonic map , a finite and possible empty set such that up to subsequences

as , with .

The convergence of to is strong in , for every . We quantify the loss of energy in the weak convergence and we show that in the case of non-constant -harmonic maps with values in one has , with a positive integer.

Cite this article

Francesca Da Lio, Compactness and bubble analysis for -harmonic maps. Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015), no. 1, pp. 201–224

DOI 10.1016/J.ANIHPC.2013.11.003