Optimal embeddings into Lorentz spaces for some vector differential operators via Gagliardo's lemma

DOI10.4171/RLM/854zbMath1442.46027arXiv1811.02691OpenAlexW3111040457WikidataQ124851142 ScholiaQ124851142MaRDI QIDQ2335816

Jean Van Schaftingen, Daniel E. Spector

Publication date: 15 November 2019

Published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.02691

zbMATH Keywords

Lorentz spacesLoomis-Whitney inequalityKorn-Sobolev inequality

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Inequalities involving derivatives and differential and integral operators (26D10) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Related Items (11)

Fine properties of functions of bounded deformation -- an approach via linear PDEs ⋮ On the complex constant rank condition and inequalities for differential operators ⋮ Boundary ellipticity and limiting \(\mathrm{L}^1\)-estimates on halfspaces ⋮ Endpoint \(L^1\) estimates for Hodge systems ⋮ Some remarks on \(L^1\) embeddings in the subelliptic setting ⋮ Symmetric gradient Sobolev spaces endowed with rearrangement-invariant norms ⋮ Phase-field approximation for a class of cohesive fracture energies with an activation threshold ⋮ New directions in harmonic analysis on \(L^1\) ⋮ Dimensional estimates and rectifiability for measures satisfying linear PDE constraints ⋮ Sobolev martingales ⋮ Sobolev inequalities for the symmetric gradient in arbitrary domains

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