We introduce n/pα-harmonic maps as critical points of the energy En;pα (v)= Rn δ α /2 v pα where pointwise v W D n → SN-1, for the N-sphere SN-1 RN and pα D n/α . This energy combines the non-local behaviour of the fractional harmonic maps introduced by Rivière and the first author with the degenerate arguments of the n-Laplacian. In this setting, we will prove Hölder continuity. © 2014 de Gruyter.
N=p-harmonic maps: Regularity for the sphere case
DA LIO, FRANCESCA;
2014
Abstract
We introduce n/pα-harmonic maps as critical points of the energy En;pα (v)= Rn δ α /2 v pα where pointwise v W D n → SN-1, for the N-sphere SN-1 RN and pα D n/α . This energy combines the non-local behaviour of the fractional harmonic maps introduced by Rivière and the first author with the degenerate arguments of the n-Laplacian. In this setting, we will prove Hölder continuity. © 2014 de Gruyter.
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