We give a positive answer to a question raised by Alberti in connection with a recent result by Brezis and Nguyen. We show the existence of currents associated with graphs of maps in trace spaces that have vanishing mean oscillation. The degree of such maps may be written in terms of these currents, of which we give some structure properties. We also deal with relevant examples.
Graphs of maps between manifolds in trace spaces and with vanishing mean oscillation / Acerbi, Emilio Daniele Giovanni; Mucci, Domenico. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - 31:5(2014), pp. 1015-1034. [10.1016/j.anihpc.2013.07.010]
Graphs of maps between manifolds in trace spaces and with vanishing mean oscillation
MUCCI, Domenico
2014
Abstract
We give a positive answer to a question raised by Alberti in connection with a recent result by Brezis and Nguyen. We show the existence of currents associated with graphs of maps in trace spaces that have vanishing mean oscillation. The degree of such maps may be written in terms of these currents, of which we give some structure properties. We also deal with relevant examples.
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