Geodesic
Hardy and Rellich type inequalities with remainders
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 1, pp. 87-110

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Hardy and Rellich type inequalities with an additional term are proved for compactly supported smooth functions on open subsets of the Euclidean space. We obtain one-dimensional Hardy type inequalities and their multidimensional analogues in convex domains with the finite inradius. We use Bessel functions and the Lamb constant. The statements proved are a generalization for the case of arbitrary $p\geq 2$ of the corresponding inequality proved by F. G. Avkhadiev, K.-J. Wirths (2011) for $p = 2$. Also we establish Rellich type inequalities on arbitrary domains, regular sets, on domains with $\theta $-cone condition and on convex domains.
DOI : 10.21136/CMJ.2021.0325-20
Classification : 26D10, 26D15
Keywords: Hardy inequality; Rellich type inequality; Bessel function; Lamb constant; distance function; Laplace operator 
@article{10_21136_CMJ_2021_0325_20,
     author = {Nasibullin, Ramil},
     title = {Hardy and {Rellich} type inequalities with remainders},
     journal = {Czechoslovak Mathematical Journal},
     pages = {87--110},
     publisher = {mathdoc},
     volume = {72},
     number = {1},
     year = {2022},
     doi = {10.21136/CMJ.2021.0325-20},
     mrnumber = {4389108},
     zbl = {07511555},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0325-20/}
}
TY  - JOUR
AU  - Nasibullin, Ramil
TI  - Hardy and Rellich type inequalities with remainders
JO  - Czechoslovak Mathematical Journal
PY  - 2022
SP  - 87
EP  - 110
VL  - 72
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0325-20/
DO  - 10.21136/CMJ.2021.0325-20
LA  - en
ID  - 10_21136_CMJ_2021_0325_20
ER  - 
%0 Journal Article
%A Nasibullin, Ramil
%T Hardy and Rellich type inequalities with remainders
%J Czechoslovak Mathematical Journal
%D 2022
%P 87-110
%V 72
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0325-20/
%R 10.21136/CMJ.2021.0325-20
%G en
%F 10_21136_CMJ_2021_0325_20
Nasibullin, Ramil. Hardy and Rellich type inequalities with remainders. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 1, pp. 87-110. doi: 10.21136/CMJ.2021.0325-20

Cité par Sources :