A Sharp Rearrangement Principle in Fourier Space and Symmetry Results for PDEs with Arbitrary Order

DOI10.1093/imrn/rnz274zbMath1481.35092arXiv1805.06294OpenAlexW3009063390WikidataQ114092275 ScholiaQ114092275MaRDI QIDQ5021586

Jérémy Sok, Enno Lenzmann

Publication date: 13 January 2022

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.06294

zbMATH Keywords

Gagliardo-Nirenberg inequalitiesAdams-Moser-Trudinger-type inequalitiesbi- and polyharmonic nonlinear Schrödinger equations (NLS)symmetric-decreasing rearrangement

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) A priori estimates in context of PDEs (35B45) Fractional partial differential equations (35R11) Symmetries, invariants, etc. in context of PDEs (35B06) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Related Items (11)

On Symmetry and Uniqueness of Ground States for Linear and Nonlinear Elliptic PDEs ⋮ Sharp critical and subcritical trace Trudinger-Moser and Adams inequalities on the upper half-spaces ⋮ Existence and non-existence of extremals for critical Adams inequality in any even dimension ⋮ Existence and nonexistence of extremals for critical Adams inequalities in \(\mathbb{R}^4\) and Trudinger-Moser inequalities in \(\mathbb{R}^2\) ⋮ Symmetry results in two-dimensional inequalities for Aharonov-Bohm magnetic fields ⋮ Existence and non-existence of ground states of bi-harmonic equations involving constant and degenerate Rabinowitz potentials ⋮ Equivalence of subcritical and critical Adams inequalities in \(W^{m,2}(\mathbb{R}^{2m})\) and existence and non-existence of extremals for Adams inequalities under inhomogeneous constraints ⋮ Block-radial symmetry breaking for ground states of biharmonic NLS ⋮ Divergent operator with degeneracy and related sharp inequalities ⋮ Sharp weighted Trudinger-Moser-Adams inequalities on the whole space and the existence of their extremals ⋮ On symmetry of traveling solitary waves for dispersion generalized NLS

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