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 and their boundaries. Then, we apply our results in order to analyze the surjectivity properties of the -harmonic extensions of VMO vector-valued functions. The operators we are dealing with are second order linear differential operators sum of squares of vector fields satisfying the hypoellipticity condition of Hörmander.
@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},
pages = {569--601},
year = {2002},
publisher = {Scuola normale superiore},
volume = {Ser. 5, 1},
number = {3},
mrnumber = {1990673},
zbl = {1109.35314},
language = {en},
url = {https://www.numdam.org/item/ASNSP_2002_5_1_3_569_0/}
}
TY - JOUR AU - Uguzzoni, Francesco AU - Lanconelli, Ermanno TI - Degree theory for VMO maps on metric spaces JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2002 SP - 569 EP - 601 VL - 1 IS - 3 PB - Scuola normale superiore UR - https://www.numdam.org/item/ASNSP_2002_5_1_3_569_0/ LA - en ID - ASNSP_2002_5_1_3_569_0 ER -
%0 Journal Article %A Uguzzoni, Francesco %A Lanconelli, Ermanno %T Degree theory for VMO maps on metric spaces %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2002 %P 569-601 %V 1 %N 3 %I Scuola normale superiore %U https://www.numdam.org/item/ASNSP_2002_5_1_3_569_0/ %G en %F 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, Série 5, Tome 1 (2002) no. 3, pp. 569-601. https://www.numdam.org/item/ASNSP_2002_5_1_3_569_0/
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