Improved Hardy-Rellich inequalities

DOI10.3934/cpaa.2022002zbMath1490.35013arXiv2106.09804OpenAlexW4205384164MaRDI QIDQ2669228

Luca Fanelli, Lucrezia Cossetti, Biagio Cassano

Publication date: 9 March 2022

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.09804

zbMATH Keywords

magnetic fieldssharp inequalitiesHardy-Rellich inequalitiesbiharmonic operatorsspherical harmonics decomposition

Mathematics Subject Classification ID

Linear operator inequalities (47A63) Inequalities involving derivatives and differential and integral operators (26D10) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Related Items (4)

Mini-workshop: Zero-range and point-like singular perturbations: for a spillover to analysis, PDE and differential geometry. Abstracts from the mini-workshop held October 2--8, 2022 ⋮ Hardy inequalities for magnetic p-Laplacians ⋮ Improved \(L^p\)-Hardy and \(L^p\)-Rellich inequalities with magnetic fields ⋮ Revisiting the Rellich inequality

Cites Work

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• Bessel pairs and optimal Hardy and Hardy-Rellich inequalities
• Confining quantum particles with a purely magnetic field
• Best constants in the Hardy-Rellich inequalities and related improvements
• On the behavior of solutions to Schrödinger equations with dipole type potentials near the singularity
• On Hardy-Rellich type inequalities in \(\mathbb R^N\)
• Sharp constants in the Hardy-Rellich inequalities
• Self-adjoint extensions for the Dirac operator with Coulomb-type spherically symmetric potentials
• Sharp Hardy-Leray inequality for curl-free fields with a remainder term
• Sharp Hardy-Leray and Rellich-Leray inequalities for curl-free vector fields
• Three-dimensional sharp Hardy-Leray inequality for solenoidal fields
• Time decay of scaling invariant electromagnetic Schrödinger equations on the plane
• Generalized Hardy inequality for the magnetic Dirichlet forms
• On the Rellich inequality with magnetic potentials
• Sharp remainder of a critical Hardy inequality
• The Hardy inequality and the heat equation with magnetic field in any dimension
• Weighted inequalities and Stein-Weiss potentials
• Improved Hardy and Rellich inequalities on Riemannian manifolds
• Factorizations and Hardy–Rellich-type inequalities
• A new proof of the Hardy–Rellich inequality in any dimension
• New sharp Hardy and Rellich type inequalities on Cartan–Hadamard manifolds and their improvements
• On the improvement of the Hardy inequality due to singular magnetic fields
• An Extension of Rellich's Inequality

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