Notre résultat principal est que pour une grande famille d’applications non linéaires entre espaces de Besov et de Sobolev, l’interpolation est un phénomène propre aux petites dimensions. Ceci prolonge des résultats obtenus précédemment par Kumlin [13] pour des applications analytiques au cas d’applications Hölder continues ou encore Lipschitz (Corollaires 1 and 2), et qui remontent aux idées de B.E.J. Dahlberg [8].
Our main result shows that for a large class of nonlinear local mappings between Besov and Sobolev space, interpolation is an exceptional low dimensional phenomenon. This extends previous results by Kumlin [13] from the case of analytic mappings to Lipschitz and Hölder continuous maps (Corollaries 1 and 2), and which go back to ideas of the late B.E.J. Dahlberg [8].
@article{AFST_2010_6_19_1_105_0,
author = {Philip Brenner and Peter Kumlin},
title = {Nonlinear {Maps} between {Besov} and {Sobolev} spaces},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {105--120},
publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 19},
number = {1},
year = {2010},
doi = {10.5802/afst.1238},
mrnumber = {2597783},
zbl = {1195.46018},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1238/}
}
TY - JOUR AU - Philip Brenner AU - Peter Kumlin TI - Nonlinear Maps between Besov and Sobolev spaces JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2010 SP - 105 EP - 120 VL - 19 IS - 1 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1238/ DO - 10.5802/afst.1238 LA - en ID - AFST_2010_6_19_1_105_0 ER -
%0 Journal Article %A Philip Brenner %A Peter Kumlin %T Nonlinear Maps between Besov and Sobolev spaces %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2010 %P 105-120 %V 19 %N 1 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1238/ %R 10.5802/afst.1238 %G en %F AFST_2010_6_19_1_105_0
Philip Brenner; Peter Kumlin. Nonlinear Maps between Besov and Sobolev spaces. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 19 (2010) no. 1, pp. 105-120. doi : 10.5802/afst.1238. https://afst.centre-mersenne.org/articles/10.5802/afst.1238/
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