Geodesic
Higher order Glaeser inequalities and optimal regularity of roots of real functions
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 12 (2013) no. 4, pp. 1001-1021

Voir la notice de l'article provenant de la source Numdam

We prove a higher order generalization of the Glaeser inequality, according to which one can estimate the first derivative of a function in terms of the function itself and the Hölder constant of its k-th derivative.

We apply these inequalities in order to obtain pointwise estimates on the derivative of the (k+α)-th root of a function of class C k whose derivative of order k is α-Hölder continuous. Thanks to such estimates, we prove that the root is not just absolutely continuous, but its derivative has a higher summability exponent.

Some examples show that our results are optimal.

Publié le :
Classification : 26A46, 26B30, 26A27 
@article{ASNSP_2013_5_12_4_1001_0,
     author = {Ghisi, Marina and Gobbino, Massimo},
     title = {Higher order {Glaeser} inequalities and optimal regularity of roots of real functions},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {1001--1021},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 12},
     number = {4},
     year = {2013},
     mrnumber = {3184577},
     zbl = {1317.26010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2013_5_12_4_1001_0/}
}
TY  - JOUR
AU  - Ghisi, Marina
AU  - Gobbino, Massimo
TI  - Higher order Glaeser inequalities and optimal regularity of roots of real functions
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 2013
SP  - 1001
EP  - 1021
VL  - 12
IS  - 4
PB  - Scuola Normale Superiore, Pisa
UR  - http://geodesic.mathdoc.fr/item/ASNSP_2013_5_12_4_1001_0/
LA  - en
ID  - ASNSP_2013_5_12_4_1001_0
ER  - 
%0 Journal Article
%A Ghisi, Marina
%A Gobbino, Massimo
%T Higher order Glaeser inequalities and optimal regularity of roots of real functions
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 2013
%P 1001-1021
%V 12
%N 4
%I Scuola Normale Superiore, Pisa
%U http://geodesic.mathdoc.fr/item/ASNSP_2013_5_12_4_1001_0/
%G en
%F ASNSP_2013_5_12_4_1001_0
Ghisi, Marina; Gobbino, Massimo. Higher order Glaeser inequalities and optimal regularity of roots of real functions. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 12 (2013) no. 4, pp. 1001-1021. http://geodesic.mathdoc.fr/item/ASNSP_2013_5_12_4_1001_0/