Geodesic
A Generalization of an Inequality of Bhattacharya and Leonetti
Canadian mathematical bulletin, Tome 39 (1996) no. 4, pp. 438-447

Voir la notice de l'article provenant de la source Cambridge University Press

We show that bounded John domains and bounded starshaped domains with respect to a point satisfy the following inequality where F: [0, ∞) → [0, ∞) is a continuous, convex function with F(0) = 0, and u is a function from an appropriate Sobolev class. Constants b and K do depend at most on D. If F(x) = xp , 1 ≤ p < ∞, this inequality reduces to the ordinary Poincaré inequality.
DOI : 10.4153/CMB-1996-052-x
Mots-clés : 46E35, 26D10, Poincaré-type inequalities, John domains, starshaped domains 
Hurri-Syrjänen, Ritva. A Generalization of an Inequality of Bhattacharya and Leonetti. Canadian mathematical bulletin, Tome 39 (1996) no. 4, pp. 438-447. doi: 10.4153/CMB-1996-052-x
@article{10_4153_CMB_1996_052_x,
     author = {Hurri-Syrj\"anen, Ritva},
     title = {A {Generalization} of an {Inequality} of {Bhattacharya} and {Leonetti}},
     journal = {Canadian mathematical bulletin},
     pages = {438--447},
     year = {1996},
     volume = {39},
     number = {4},
     doi = {10.4153/CMB-1996-052-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1996-052-x/}
}
TY  - JOUR
AU  - Hurri-Syrjänen, Ritva
TI  - A Generalization of an Inequality of Bhattacharya and Leonetti
JO  - Canadian mathematical bulletin
PY  - 1996
SP  - 438
EP  - 447
VL  - 39
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1996-052-x/
DO  - 10.4153/CMB-1996-052-x
ID  - 10_4153_CMB_1996_052_x
ER  - 
%0 Journal Article
%A Hurri-Syrjänen, Ritva
%T A Generalization of an Inequality of Bhattacharya and Leonetti
%J Canadian mathematical bulletin
%D 1996
%P 438-447
%V 39
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1996-052-x/
%R 10.4153/CMB-1996-052-x
%F 10_4153_CMB_1996_052_x

[1] 1. Bhattacharya, T. and Leonetti, F., A new Poincaré inequality and its application to the regularity ofminimizers of integral functionah with nonstandard growth, Nonlinear Anal. 17(1991), 833–839. Google Scholar

[2] 2. Gehring, F. W. and Martio, O., Lipschitz classes and quasiconformal mappings, Ann. Acad. Sci. Fenn., Series A. I. Math. 10(1985), 203–219. Google Scholar

[3] 3. Hurri, R., Poincaré domains in R”, Ann. Acad. Sci. Fenn. Ser. AI Math. Dissertationes 71(1988), 1—42. Google Scholar

[4] 4. Martio, O., John domains, bilipschitz balls and Poincaré inequality, Rev. Roumaine Math. Pures Appl. 33(1988), 107–112. Google Scholar

[5] 5. Maz'ya, V. G., Sobolev spaces, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1985. Google Scholar

[6] 6. Stein, E. M., Singular integrals and differentiability properties of functions, Princeton University Press, Princeton, New Jersey, 1970. Google Scholar

Cité par Sources :