Sharp affine weighted 𝐿^{𝑝} Sobolev type inequalities

DOI10.1090/tran/7728zbMath1436.46037arXiv1708.09471OpenAlexW2963581674MaRDI QIDQ5227967

Marcos Montenegro, Carlos Hugo Jiménez, Julian Haddad

Publication date: 7 August 2019

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.09471

zbMATH Keywords

convex bodySobolev inequalitycentroid bodies

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Inequalities and extremum problems involving convexity in convex geometry (52A40) Convex sets without dimension restrictions (aspects of convex geometry) (52A05)

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Cites Work

• Unnamed Item
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• Sharp affine Sobolev type inequalities via the \(L_{p}\) Busemann-Petty centroid inequality
• The affine Sobolev-Zhang inequality on BV(\(\mathbb R^n)\)
• Sharp isoperimetric inequalities via the ABP method
• Sharp convex Lorentz-Sobolev inequalities
• An asymmetric affine Pólya-Szegő principle
• An integral formula for total gradient variation
• Centroid surfaces
• Best constant in Sobolev trace inequalities on the half-space
• From Brunn-Minkowski to sharp Sobolev inequalities
• General \(L_{p}\) affine isoperimetric inequalities
• Affine Moser-Trudinger and Morrey-Sobolev inequalities
• On some affine isoperimetric inequalities
• Best constant in Sobolev inequality
• Problèmes isoperimetriques et espaces de Sobolev
• Blaschke-Santaló inequalities
• The general optimal \(L^{p}\)-Euclidean logarithmic Sobolev inequality by Hamilton--Jacobi equations.
• Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions.
• A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities.
• The \(L^p\)-Busemann-Petty centroid inequality
• The affine Sobolev inequality.
• \(L_ p\) affine isoperimetric inequalities.
• Sharp affine \(L_ p\) Sobolev inequalities.
• The optimal Euclidean \(L^{p}\)-Sobolev logarithmic inequality.
• Asymmetric affine \(L_p\) Sobolev inequalities
• The affine Pólya-Szegö principle: equality cases and stability
• Normal and integral currents
• Sobolev and isoperimetric inequalities with monomial weights
• Geometric asymptotics and the logarithmic Sobolev inequality
• On the $L_{p}$-Minkowski problem
• Analysis and Geometry of Markov Diffusion Operators
• Sharp weighted Sobolev and Gagliardo–Nirenberg inequalities on half-spaces via mass transport and consequences
• Convex Bodies The Brunn-MinkowskiTheory
• Optimal Sobolev norms and the Lp Minkowski problem
• The weighted Sobolev and mean value inequalities

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