We investigate geometric curvature energies on closed curves involving integral versions of the Menger curvature. In particular, we prove geometric variants of Morrey-Sobolev and Morrey-space imbedding theorems, which may be viewed as counterparts to respective results on one-dimensional sets in the context of harmonic analysis.
@article{ASNSP_2010_5_9_1_145_0,
author = {Strzelecki, Pawe{\l} and Szuma\'nska, Marta and von der Mosel, Heiko},
title = {Regularizing and self-avoidance effects of integral {Menger} curvature},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {145--187},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 9},
number = {1},
year = {2010},
mrnumber = {2668877},
zbl = {1193.28007},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2010_5_9_1_145_0/}
}
TY - JOUR AU - Strzelecki, Paweł AU - Szumańska, Marta AU - von der Mosel, Heiko TI - Regularizing and self-avoidance effects of integral Menger curvature JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2010 SP - 145 EP - 187 VL - 9 IS - 1 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2010_5_9_1_145_0/ LA - en ID - ASNSP_2010_5_9_1_145_0 ER -
%0 Journal Article %A Strzelecki, Paweł %A Szumańska, Marta %A von der Mosel, Heiko %T Regularizing and self-avoidance effects of integral Menger curvature %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2010 %P 145-187 %V 9 %N 1 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2010_5_9_1_145_0/ %G en %F ASNSP_2010_5_9_1_145_0
Strzelecki, Paweł; Szumańska, Marta; von der Mosel, Heiko. Regularizing and self-avoidance effects of integral Menger curvature. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 1, pp. 145-187. http://www.numdam.org/item/ASNSP_2010_5_9_1_145_0/
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