JournalsaihpcVol. 31, No. 5pp. 1015–1034

Graphs of maps between manifolds in trace spaces and with vanishing mean oscillation

  • Emilio Acerbi

    Dipartimento di Matematica e Informatica, Università di Parma, Parco Area delle Scienze 53/A, I-43124 Parma, Italy

  • Domenico Mucci

    Dipartimento di Matematica e Informatica, Università di Parma, Parco Area delle Scienze 53/A, I-43124 Parma, Italy
Graphs of maps between manifolds in trace spaces and with vanishing mean oscillation cover
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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.

Cite this article

Emilio Acerbi, Domenico Mucci, Graphs of maps between manifolds in trace spaces and with vanishing mean oscillation. Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), no. 5, pp. 1015–1034

DOI 10.1016/J.ANIHPC.2013.07.010