Improved Hardy-Rellich inequalities
We investigate Hardy-Rellich inequalities for perturbed Laplacians. In particular, we show that a non-trivial angular perturbation of the free operator typically improves the inequality, and may also provide an estimate which does not hold in the free case. The main examples are related to the intro...
Published in: | Communications on Pure & Applied Analysis |
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ftuncampaniairis:oai:iris.unicampania.it:11591/461291 2024-02-11T10:05:38+01:00 Improved Hardy-Rellich inequalities Cassano, Biagio Cossetti, Lucrezia Fanelli, Luca Cassano, Biagio Cossetti, Lucrezia Fanelli, Luca 2022 http://hdl.handle.net/11591/461291 https://doi.org/10.3934/cpaa.2022002 eng eng info:eu-repo/semantics/altIdentifier/wos/WOS:000731360400001 volume:21 issue:3 firstpage:867 lastpage:889 numberofpages:23 journal:COMMUNICATIONS ON PURE AND APPLIED ANALYSIS http://hdl.handle.net/11591/461291 doi:10.3934/cpaa.2022002 info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-85123008975 Hardy-Rellich inequalitie Biharmonic operator magnetic field sharp inequalitie spherical harmonics decomposition info:eu-repo/semantics/article 2022 ftuncampaniairis https://doi.org/10.3934/cpaa.2022002 2024-01-23T23:17:51Z We investigate Hardy-Rellich inequalities for perturbed Laplacians. In particular, we show that a non-trivial angular perturbation of the free operator typically improves the inequality, and may also provide an estimate which does not hold in the free case. The main examples are related to the introduction of a magnetic field: this is a manifestation of the diamagnetic phenomenon, which has been observed by Laptev and Weidl in [21] for the Hardy inequality, later by Evans and Lewis in [9] for the Rellich inequality; however, to the best of our knowledge, the so called Hardy-Rellich inequality has not yet been investigated in this regards. After showing the optimal inequality, we prove that the best constant is not attained by any function in the domain of the estimate. Article in Journal/Newspaper laptev Università degli Studi della Campania "Luigi Vanvitelli": CINECA IRIS V: Communications on Pure & Applied Analysis 0 0 0 |
institution |
Open Polar |
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Università degli Studi della Campania "Luigi Vanvitelli": CINECA IRIS V: |
op_collection_id |
ftuncampaniairis |
language |
English |
topic |
Hardy-Rellich inequalitie Biharmonic operator magnetic field sharp inequalitie spherical harmonics decomposition |
spellingShingle |
Hardy-Rellich inequalitie Biharmonic operator magnetic field sharp inequalitie spherical harmonics decomposition Cassano, Biagio Cossetti, Lucrezia Fanelli, Luca Improved Hardy-Rellich inequalities |
topic_facet |
Hardy-Rellich inequalitie Biharmonic operator magnetic field sharp inequalitie spherical harmonics decomposition |
description |
We investigate Hardy-Rellich inequalities for perturbed Laplacians. In particular, we show that a non-trivial angular perturbation of the free operator typically improves the inequality, and may also provide an estimate which does not hold in the free case. The main examples are related to the introduction of a magnetic field: this is a manifestation of the diamagnetic phenomenon, which has been observed by Laptev and Weidl in [21] for the Hardy inequality, later by Evans and Lewis in [9] for the Rellich inequality; however, to the best of our knowledge, the so called Hardy-Rellich inequality has not yet been investigated in this regards. After showing the optimal inequality, we prove that the best constant is not attained by any function in the domain of the estimate. |
author2 |
Cassano, Biagio Cossetti, Lucrezia Fanelli, Luca |
format |
Article in Journal/Newspaper |
author |
Cassano, Biagio Cossetti, Lucrezia Fanelli, Luca |
author_facet |
Cassano, Biagio Cossetti, Lucrezia Fanelli, Luca |
author_sort |
Cassano, Biagio |
title |
Improved Hardy-Rellich inequalities |
title_short |
Improved Hardy-Rellich inequalities |
title_full |
Improved Hardy-Rellich inequalities |
title_fullStr |
Improved Hardy-Rellich inequalities |
title_full_unstemmed |
Improved Hardy-Rellich inequalities |
title_sort |
improved hardy-rellich inequalities |
publishDate |
2022 |
url |
http://hdl.handle.net/11591/461291 https://doi.org/10.3934/cpaa.2022002 |
genre |
laptev |
genre_facet |
laptev |
op_relation |
info:eu-repo/semantics/altIdentifier/wos/WOS:000731360400001 volume:21 issue:3 firstpage:867 lastpage:889 numberofpages:23 journal:COMMUNICATIONS ON PURE AND APPLIED ANALYSIS http://hdl.handle.net/11591/461291 doi:10.3934/cpaa.2022002 info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-85123008975 |
op_doi |
https://doi.org/10.3934/cpaa.2022002 |
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Communications on Pure & Applied Analysis |
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1790602739269500928 |