Geodesic
A new characterization of chord-arc domains
Journal of the European Mathematical Society, Tome 19 (2017) no. 4, pp. 967-981.

Voir la notice de l'article provenant de la source EMS Press

We show that if Ω⊂Rn+1, n≥1, is a uniform domain (also known as a 1-sided NTA domain), i.e., a domain which enjoys interior Corkscrew and Harnack Chain conditions, then uniform rectifiability of the boundary of Ω implies the existence of exterior corkscrew points at all scales, so that in fact, Ω is a chord-arc domain, i.e., a domain with an Ahlfors-David regular boundary which satisfies both interior and exterior corkscrew conditions, and an interior Harnack chain condition. We discuss some implications of this result for theorems of F. and M. Riesz type, and for certain free boundary problems.
DOI : 10.4171/jems/685
Classification : 28-XX, 31-XX, 35-XX, 42-XX
Keywords: Chord-arc domains, NTA domains, 1-sided NTA domains, uniform domains, uniform rectifiability, Carleson measures, harmonic measure, A∞​ Muckenhoupt weights 
@article{JEMS_2017_19_4_a1,
     author = {Jonas Azzam and Steve Hofmann and Jos\'e Mar{\'\i}a Martell and Kaj Nystr\"om and Tatiana Toro},
     title = {A new characterization of chord-arc domains},
     journal = {Journal of the European Mathematical Society},
     pages = {967--981},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {2017},
     doi = {10.4171/jems/685},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/685/}
}
TY  - JOUR
AU  - Jonas Azzam
AU  - Steve Hofmann
AU  - José María Martell
AU  - Kaj Nyström
AU  - Tatiana Toro
TI  - A new characterization of chord-arc domains
JO  - Journal of the European Mathematical Society
PY  - 2017
SP  - 967
EP  - 981
VL  - 19
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/685/
DO  - 10.4171/jems/685
ID  - JEMS_2017_19_4_a1
ER  - 
%0 Journal Article
%A Jonas Azzam
%A Steve Hofmann
%A José María Martell
%A Kaj Nyström
%A Tatiana Toro
%T A new characterization of chord-arc domains
%J Journal of the European Mathematical Society
%D 2017
%P 967-981
%V 19
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/685/
%R 10.4171/jems/685
%F JEMS_2017_19_4_a1
Jonas Azzam; Steve Hofmann; José María Martell; Kaj Nyström; Tatiana Toro. A new characterization of chord-arc domains. Journal of the European Mathematical Society, Tome 19 (2017) no. 4, pp. 967-981. doi : 10.4171/jems/685. http://geodesic.mathdoc.fr/articles/10.4171/jems/685/

Cité par Sources :