Degree theory for VMO maps on metric spaces
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 1 (2002) no. 3, p. 569-601

We construct a degree theory for Vanishing Mean Oscillation functions in metric spaces, following some ideas of Brezis & Nirenberg. The underlying sets of our metric spaces are bounded open subsets of N and their boundaries. Then, we apply our results in order to analyze the surjectivity properties of the L-harmonic extensions of VMO vector-valued functions. The operators L we are dealing with are second order linear differential operators sum of squares of vector fields satisfying the hypoellipticity condition of Hörmander.

Classification:  35H20,  47H11,  43A85
@article{ASNSP_2002_5_1_3_569_0,
     author = {Uguzzoni, Francesco and Lanconelli, Ermanno},
     title = {Degree theory for VMO maps on metric spaces},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 5, 1},
     number = {3},
     year = {2002},
     pages = {569-601},
     zbl = {1109.35314},
     mrnumber = {1990673},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2002_5_1_3_569_0}
}
Uguzzoni, Francesco; Lanconelli, Ermanno. Degree theory for VMO maps on metric spaces. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 1 (2002) no. 3, pp. 569-601. http://www.numdam.org/item/ASNSP_2002_5_1_3_569_0/

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