Affine Moser-Trudinger and Morrey-Sobolev inequalities

DOI10.1007/s00526-009-0235-4zbMath1202.26029OpenAlexW1964075765MaRDI QIDQ1047926

Gaoyong Zhang, Erwin Lutwak, Deane Yang, Andrea Cianchi

Publication date: 8 January 2010

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-009-0235-4

zbMATH Keywords

convex bodiesMoser-Trudinger inequalityBrunn-Minkowski theory

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (only showing first 100 items - show all)

Some variants of the Hardy inequality ⋮ Lp$L_p$‐cosine transform of the (p,q)${(p,q)}$‐th dual curvature measure ⋮ Sharp norm estimates for functional dual affine quermassintegrals ⋮ On the polar Orlicz-Minkowski problems and the p-capacitary Orlicz-Petty bodies ⋮ The affine convex Lorentz-Sobolev inequalities ⋮ Affine fractional \(L^p\) Sobolev inequalities ⋮ Projection body and isoperimetric inequalities for \(s\)-concave functions ⋮ Towards existence theorems to affine \(p\)-Laplace equations via variational approach ⋮ Continuity of the solution to the even Lp Minkowski problem for 0 < p < 1 in the plane ⋮ $\mathrm {SL}(n)$-contravariant $L_p$-Minkowski valuations ⋮ On Complex L_p affine isoperimetric inequalities ⋮ The logarithmic Minkowski problem for non-symmetric measures ⋮ SL(n)-covariantL_p-Minkowski valuations ⋮ The logarithmic Minkowski problem ⋮ Sharp affine weighted 𝐿^{𝑝} Sobolev type inequalities ⋮ The cone Moser–Trudinger inequalities and applications ⋮ Sharp affine Trudinger–Moser inequalities: A new argument ⋮ Mirror symmetric solutions to the centro-affine Minkowski problem ⋮ The \(L_{p}\)-Minkowski problem for \(-n < p < 1\) ⋮ Sharp singular Trudinger-Moser inequalities in Lorentz-Sobolev spaces ⋮ On the \(L_p\) dual Minkowski problem ⋮ New approach to the affine Pólya-Szegö principle and the stability version of the affine Sobolev inequality ⋮ Minkowski valuations under volume constraints ⋮ Fourier analysis and optimal Hardy-Adams inequalities on hyperbolic spaces of any even dimension ⋮ Fractional Besov trace/extension-type inequalities via the Caffarelli-Silvestre extension ⋮ Sharp Hardy-Sobolev-Maz'ya, Adams and Hardy-Adams inequalities on the Siegel domains and complex hyperbolic spaces ⋮ Centro–affine curvature flows on centrally symmetric convex curves ⋮ The Centro-Affine Hadwiger Theorem ⋮ Multiple solutions of the \(L_{p}\)-Minkowski problem ⋮ The equality cases in Steiner's projection inequality ⋮ On the uniqueness and continuity of the dual area measure ⋮ Finsler Trudinger-Moser inequalities on \(\mathbb{R}^2\) ⋮ Affine Orlicz Pólya-Szegő principle for log-concave functions ⋮ Minimization to the Zhang's energy on \(BV (\Omega)\) and sharp affine Poincaré-Sobolev inequalities ⋮ \(L_p\)-curvature measures and \(L_{p, q}\)-mixed volumes ⋮ On the \(L^p\) Aleksandrov problem for negative \(p\) ⋮ Sharp Hardy-Adams inequalities for bi-Laplacian on hyperbolic space of dimension four ⋮ Equivalence of the local and global versions of the \(L^p\)-Brunn-Minkowski inequality ⋮ Orlicz-Lorentz centroid bodies ⋮ Existence and nonexistence of extremals for critical Adams inequalities in \(\mathbb{R}^4\) and Trudinger-Moser inequalities in \(\mathbb{R}^2\) ⋮ The sharp affine \(L_2\) Sobolev trace inequality and affine energy in the fractional Sobolev spaces ⋮ The Hadamard variational formula and the Minkowski problem for \(p\)-capacity ⋮ Note on affine Gagliardo-Nirenberg inequalities ⋮ Minkowski valuations on convex functions ⋮ The Brunn-Minkowski-Firey inequality for nonconvex sets ⋮ The Orlicz centroid inequality for star bodies ⋮ Relative \(\infty\)-capacity and its affinization ⋮ Continuity of the solution to the \(L_p\) Minkowski problem in Gaussian probability space ⋮ Optimal Sobolev norms in the affine class ⋮ A generalized rotationally symmetric case of the centroaffine Minkowski problem ⋮ Convex geometry and its applications. Abstracts from the workshop held December 12--18, 2021 (hybrid meeting) ⋮ Asymmetric \(L_p\) convexification and the convex Lorentz-Sobolev inequality ⋮ The affine Sobolev-Zhang inequality on BV(\(\mathbb R^n)\) ⋮ The affine Pólya-Szegö principle: equality cases and stability ⋮ The minimal affine total variation on \(BV(\mathbb{R}^n)\) ⋮ Sharp geometric inequalities for the general \(p\)-affine capacity ⋮ Minkowski additive operators under volume constraints ⋮ The dual Orlicz-Minkowski problem ⋮ On the Orlicz Minkowski problem for polytopes ⋮ The \(L_p\) Minkowski problem for the electrostatic \(\mathfrak{p}\)-capacity ⋮ The log-Brunn-Minkowski inequality ⋮ \(L_p\) mixed geominimal surface area ⋮ A new capacity for the affine bounded variation ⋮ Stability in the \(L_p\) Shephard problem ⋮ On the stability of the \(p\)-affine isoperimetric inequality ⋮ The Orlicz Brunn-Minkowski inequality ⋮ New geometric aspects of Moser-Trudinger inequalities on Riemannian manifolds: the non-compact case ⋮ Orlicz-Minkowski flows ⋮ An asymmetric affine Pólya-Szegő principle ⋮ \(L_{p}\) dual curvature measures ⋮ Affine Poisson \& non-Poisson trace principles for \(\dot{H}^{- 1 < - \alpha \leq - \frac{ 1}{ 2}}(\mathbb{R}^{n - 1 \geq 2})\) ⋮ Continuity of the solution to the dual Minkowski problem for negative indices ⋮ The sharp affine \(L^2\) Sobolev trace inequality and variants ⋮ Compactness properties and ground states for the affine Laplacian ⋮ Sharp affine and improved Moser-Trudinger-Adams type inequalities on unbounded domains in the spirit of Lions ⋮ The logarithmic Minkowski problem for polytopes ⋮ An optimal Hardy-Morrey inequality ⋮ Sharp convex Lorentz-Sobolev inequalities ⋮ Centro-affine tensor valuations ⋮ On the \(L_{p}\) Monge-Ampère equation ⋮ Minkowski valuations intertwining the special linear group ⋮ General affine surface areas ⋮ The even Orlicz Minkowski problem ⋮ Complex affine isoperimetric inequalities ⋮ Affine Fisher information inequalities ⋮ General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski problem. II ⋮ The \(L^p\) Gagliardo-Nirenberg-Zhang inequality ⋮ Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems ⋮ Extremal functions for Morrey's inequality ⋮ From affine Poincaré inequalities to affine spectral inequalities ⋮ On the mixed Pólya-Szegö principle ⋮ The relative 𝑝-affine capacity ⋮ A functional Busemann intersection inequality ⋮ Critical and subcritical Trudinger-Moser inequalities on complete noncompact Riemannian manifolds ⋮ The Petty projection inequality for sets of finite perimeter ⋮ Sharp Sobolev inequalities via projection averages ⋮ General \((p,q)\)-mixed projection bodies ⋮ Smoothness in the \(L_p\) Minkowski problem for \(p<1\) ⋮ ISOPERIMETRIC INEQUALITIES FOR L_p GEOMINIMAL SURFACE AREA ⋮ Valuations on function spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A new proof of a sharp inequality concerning the Dirichlet integral
• The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
• Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
• Moser type inequalities for higher-order derivatives in Lorentz spaces
• Rearrangements and convexity of level sets in PDE
• On the isoperimetric nature of a rearrangement inequality and its consequences for some variational problems
• A sharp inequality of J. Moser for higher order derivatives
• Extremal functions for the Trudinger-Moser inequality in 2 dimensions
• Best constant in Sobolev inequality
• Problèmes isoperimetriques et espaces de Sobolev
• Sharp borderline Sobolev inequalities on compact Riemannian manifolds
• Ellipsoids and matrix-valued valuations
• Fundamental solution for the \(Q\)-Laplacian and sharp Moser--Trudinger inequality in Carnot groups.
• On the \(p\)-affine surface area
• A new ellipsoid associated with convex bodies
• The \(L^p\)-Busemann-Petty centroid inequality
• The discrete planar \(L_0\)-Minkowski problem
• The affine Sobolev inequality.
• \(L_ p\) affine isoperimetric inequalities.
• A sharp Trudinger-Moser type inequality for unbounded domains in \(\mathbb R^2\)
• Sharp affine \(L_ p\) Sobolev inequalities.
• The Cramer-Rao inequality for star bodies
• Functions of bounded variation and rearrangements
• Surface bodies and \(p\)-affine surface area
• On the Christoffel-Minkowski problem of Firey's \(p\)-sum
• Convex rearrangement: Equality cases in the Pólya-Szegö inequality
• On the regularity of solutions to a generalization of the Minkowski problem
• The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
• Moser-type inequalities in Lorentz spaces
• \(L_p\) Minkowski problem with not necessarily positive data
• Moser--Trudinger trace inequalities
• Steiner symmetric extremals in Pólya-Szegő-type inequalities
• The \(L_p\)-Minkowski problem and the Minkowski problem in centroaffine geometry
• Normal and integral currents
• ON THE HIGHER ORDER CONFORMAL COVARIANT OPERATORS ON THE SPHERE
• Rearrangements of functions and convergence in orlicz spaces
• The Brunn-Minkowski inequality
• Best constants for Moser-Trudinger inequalities on the Heisenberg group
• On an inequality by N. Trudinger and J. Moser and related elliptic equations
• On the $L_{p}$-Minkowski problem
• Fourier transform and Firey projections of convex bodies
• Extremal functions for Moser’s inequality
• Moser-Trudinger inequalities without boundary conditions and isoperimetric problems
• Minkowski valuations
• Optimal Sobolev norms and the Lp Minkowski problem

This page was built for publication: Affine Moser-Trudinger and Morrey-Sobolev inequalities