| Title:
|
Hardy and Rellich type inequalities with remainders (English) |
| Author:
|
Nasibullin, Ramil |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
72 |
| Issue:
|
1 |
| Year:
|
2022 |
| Pages:
|
87-110 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Hardy inequality |
| Keyword:
|
Rellich type inequality |
| Keyword:
|
Bessel function |
| Keyword:
|
Lamb constant |
| Keyword:
|
distance function |
| Keyword:
|
Laplace operator |
| MSC:
|
26D10 |
| MSC:
|
26D15 |
| idZBL:
|
Zbl 07511555 |
| idMR:
|
MR4389108 |
| DOI:
|
10.21136/CMJ.2021.0325-20 |
| . |
| Date available:
|
2022-03-25T08:27:00Z |
| Last updated:
|
2024-04-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149575 |
| . |
| Reference:
|
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