A weighted Trudinger-Moser inequality on \(\mathbb{R}^N\) and its application to Grushin operator

DOI10.1007/s10114-020-9122-xzbMath1448.35142OpenAlexW3016157156MaRDI QIDQ1987547

Yanyan Li

Publication date: 15 April 2020

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-020-9122-x

zbMATH Keywords

Trudinger-Moser inequality\(H\)-type groupGrushin operator

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Variational methods for second-order elliptic equations (35J20)

Related Items (1)

Existence of the solution for a class of the semilinear degenerate elliptic equation involving the Grushin operator in R2$\mathbb {R}^2$: The interaction between Grushin's critical exponent and exponential growth

Cites Work

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• Sharp Moser-Trudinger inequalities on Riemannian manifolds with negative curvature
• Sharp constants for weighted Moser-Trudinger inequalities on groups of Heisenberg type
• A sharp Trudinger-Moser inequality on any bounded and convex planar domain
• Trudinger-Moser inequalities on complete noncompact Riemannian manifolds
• A sharp inequality of J. Moser for higher order derivatives
• Sharp borderline Sobolev inequalities on compact Riemannian manifolds
• Generalized Heisenberg groups and Damek-Ricci harmonic spaces
• Fundamental solution for the \(Q\)-Laplacian and sharp Moser--Trudinger inequality in Carnot groups.
• Nonlinear Liouville theorems for some critical problems on \(H\)-type groups.
• Polar coordinates in Carnot groups
• Fourier analysis and optimal Hardy-Adams inequalities on hyperbolic spaces of any even dimension
• New geometric aspects of Moser-Trudinger inequalities on Riemannian manifolds: the non-compact case
• Sharp Moser-Trudinger inequality on the Heisenberg group at the critical case and applications
• A sharp Trudinger-Moser type inequality for unbounded domains in \(\mathbb R^2\)
• Isoperimetric inequality in the Grushin plane
• Symmetry properties of positive entire solutions of Yamabe-type equations on groups of Heisenberg type
• Singular solutions, homogeneous norms, and quasiconformal mappings in Carnot groups
• Best constants for Moser-Trudinger inequalities, fundamental solutions and one-parameter representation formulas on groups of Heisenberg type
• Trudinger-Moser inequalities on harmonic \(A N\) groups under Lorentz norms
• Sharp Hardy-Adams inequalities for bi-Laplacian on hyperbolic space of dimension four
• Trudinger-Moser inequalities on hyperbolic spaces under Lorentz norms
• Kelvin transform for Grushin operators and critical semilinear equations
• Sharp weighted Young's inequalities and Moser-Trudinger inequalities on Heisenberg type groups and Grushin spaces
• Convolution operators and L(p, q) spaces
• A new approach to sharp Moser-Trudinger and Adams type inequalities: a rearrangement-free argument
• On the Grushin operator and hyperbolic symmetry
• Sobolev Inequalities for Weighted Gradients
• Fundamental Solutions for a Class of Hypoelliptic PDE Generated by Composition of Quadratic Forms
• Hardy inequalities related to Grushin type operators
• Best constants for Moser-Trudinger inequalities on the Heisenberg group
• Paneitz operators on hyperbolic spaces and high order Hardy-Sobolev-Maz'ya inequalities on half spaces
• A sharp Trudinger-Moser type inequality for unbounded domains in $\mathbb{R}^n$

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