Compactness and bubble analysis for -harmonic maps
Francesca Da Lio
Department of Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland
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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