A mass transportation approach for Sobolev inequalities in variable exponent spaces

DOI10.1007/s00229-016-0830-6zbMath1360.46025arXiv1503.02943OpenAlexW1597276590MaRDI QIDQ304491

Juan Pablo Borthagaray, Julián Fernández Bonder, Analia Silva

Publication date: 25 August 2016

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.02943

zbMATH Keywords

Sobolev-Poincaré inequalityvariable exponent spacesSobolev-trace inequality

Mathematics Subject Classification ID

Variational inequalities (49J40) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Cites Work

• Lebesgue and Sobolev spaces with variable exponents
• Best constant in Sobolev trace inequalities on the half-space
• Sobolev inequalities with variable exponent attaining the values 1 and \(n\)
• Conformal deformation of a Riemannian metric to a scalar flat metric with constant mean curvature on the boundary
• A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities.
• Existence and uniqueness of monotone measure-preserving maps
• Boundary trace embedding theorems for variable exponent Sobolev spaces
• Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spacesLp(·) andWk,p(·)
• Polar factorization and monotone rearrangement of vector‐valued functions
• Sobolev embeddings with variable exponent
• Optimal Transport
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