Degree theory for VMO maps on metric spaces

Francesco Uguzzoni; Ermanno Lanconelli

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2002)

  • Volume: 1, Issue: 3, page 569-601
  • ISSN: 0391-173X

Abstract

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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.

How to cite

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Uguzzoni, Francesco, and Lanconelli, Ermanno. "Degree theory for VMO maps on metric spaces." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 1.3 (2002): 569-601. <http://eudml.org/doc/84481>.

@article{Uguzzoni2002,
abstract = {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 $\mathbb \{R\}^N$ 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.},
author = {Uguzzoni, Francesco, Lanconelli, Ermanno},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {trace problem},
language = {eng},
number = {3},
pages = {569-601},
publisher = {Scuola normale superiore},
title = {Degree theory for VMO maps on metric spaces},
url = {http://eudml.org/doc/84481},
volume = {1},
year = {2002},
}

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
PB - Scuola normale superiore
VL - 1
IS - 3
SP - 569
EP - 601
AB - 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 $\mathbb {R}^N$ 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.
LA - eng
KW - trace problem
UR - http://eudml.org/doc/84481
ER -

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