Classification of solutions of an equation related to a conformal log Sobolev inequality

DOI10.1016/j.aim.2020.107395zbMath1453.35036arXiv2003.08135OpenAlexW3081523297MaRDI QIDQ2213782

Rupert L. Frank, Tobias König, Hanli Tang

Publication date: 3 December 2020

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.08135

zbMATH Keywords

conformal invariancelog-Sobolev inequalityclassification of solutionsmethod of moving spheres

Mathematics Subject Classification ID

Maximum principles in context of PDEs (35B50) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23) Integro-partial differential equations (35R09)

Related Items (9)

Small order asymptotics for nonlinear fractional problems ⋮ Classification of solutions to mixed order conformally invariant systems in \({\mathbb{R}}^2\) ⋮ Small order limit of fractional Dirichlet sublinear-type problems ⋮ Classification of solutions for mixed order conformally system with Hartree-type nonlinearity in ℝn ⋮ Classification of Solutions to Conformally Invariant Systems with Mixed Order and Exponentially Increasing or Nonlocal Nonlinearity ⋮ Sharp stability of log-Sobolev and Moser-Onofri inequalities on the sphere ⋮ Bounds for eigenvalues of the Dirichlet problem for the logarithmic Laplacian ⋮ Symmetry of positive solutions for Lane-Emden systems involving the logarithmic Laplacian ⋮ Reverse conformally invariant Sobolev inequalities on the sphere

Cites Work

• Unnamed Item
• A fractional Yamabe flow and some applications
• A direct method of moving planes for the fractional Laplacian
• Intrinsic scaling properties for nonlocal operators
• Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
• Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
• Classification of positive solitary solutions of the nonlinear Choquard equation
• Liouville-type theorems and harnack-type inequalities for semilinear elliptic equations
• Remark on some conformally invariant integral equations: the method of moving spheres
• Uniqueness theorems through the method of moving spheres
• \(\mathit\Gamma\)-convergence of the Heitmann-Radin sticky disc energy to the crystalline perimeter
• A direct method of moving spheres on fractional order equations
• A New, Rearrangement-free Proof of the Sharp Hardy–Littlewood–Sobolev Inequality
• Conformally Invariant Powers of the Laplacian, I: Existence
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• Sobolev inequalities, the Poisson semigroup, and analysis on the sphere Sn.
• Logarithmic Sobolev inequalities and the existence of singular integrals
• The Dirichlet problem for the logarithmic Laplacian
• Classification of solutions for an integral equation
• Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality
• Symmetry via antisymmetric maximum principles in nonlocal problems of variable order

This page was built for publication: Classification of solutions of an equation related to a conformal log Sobolev inequality