The Hardy inequality and the heat equation with magnetic field in any dimension

DOI10.1080/03605302.2016.1179317zbMath1353.35244arXiv1409.6433OpenAlexW85266298MaRDI QIDQ2833271

Cristian Cazacu, David Krejčiřík

Publication date: 17 November 2016

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.6433

zbMATH Keywords

heat equationHardy inequalitymagnetic Schrödinger operatorlarge time behaviour of solutionsAharonov-Bohm magnetic field

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Heat equation (35K05) Asymptotic distributions of eigenvalues in context of PDEs (35P20) PDEs in connection with quantum mechanics (35Q40) Schrödinger operator, Schrödinger equation (35J10) Asymptotic analysis for problems in thermodynamics and heat transfer (80M35) Self-similar solutions to PDEs (35C06) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Related Items (17)

Sharp second order uncertainty principles ⋮ Absence of eigenvalues of two-dimensional magnetic Schrödinger operators ⋮ Improved Hardy-Rellich inequalities ⋮ The Hardy inequality and large time behaviour of the heat equation on \(\mathbb{R}^{N - k} \times ( 0 , \infty )^k\) ⋮ Horizontal magnetic fields and improved Hardy inequalities in the Heisenberg group ⋮ Hardy inequalities for magnetic p-Laplacians ⋮ Improved \(L^p\)-Hardy and \(L^p\)-Rellich inequalities with magnetic fields ⋮ Hypoelliptic operators in geometry. Abstracts from the workshop held May 21--26, 2023 ⋮ On the improvement of the Hardy inequality due to singular magnetic fields ⋮ Complex Magnetic Fields: An Improved Hardy--Laptev--Weidl Inequality and Quasi-Self-Adjointness ⋮ Orbital stability for the Schrödinger operator involving inverse square potential ⋮ Improved time-decay for a class of scaling critical electromagnetic Schrödinger flows ⋮ Absence of eigenvalues of Dirac and Pauli Hamiltonians via the method of multipliers ⋮ The asymptotic behaviour of the heat equation in a sheared unbounded strip ⋮ Spectral transitions for Aharonov-Bohm Laplacians on conical layers ⋮ On an extension of the Iwatsuka model ⋮ On parabolic equations with critical electromagnetic potentials

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