Degree theory for VMO maps on metric spaces

Uguzzoni, Francesco; Lanconelli, Ermanno

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 3, pp. 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 ${ℝ}^N$ 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

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