On improved fractional Sobolev-Poincaré inequalities

DOI10.1007/s11512-015-0227-xzbMath1362.35012arXiv1312.5118OpenAlexW50578759WikidataQ110020192 ScholiaQ110020192MaRDI QIDQ517234

Antti V. Vähäkangas, Bartłomiej Dyda, Lizaveta Ihnatsyeva

Publication date: 23 March 2017

Published in: Arkiv för Matematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.5118

zbMATH Keywords

John domainsweak and strong type inequalities

Mathematics Subject Classification ID

Fractional partial differential equations (35R11) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Related Items (17)

Fractional Sobolev-Poincaré inequalities in irregular domains ⋮ Improved Poincar\'e inequalities in fractional Sobolev spaces ⋮ A tribute to Pola Harboure: Isoperimetric inequalities and the HMS extrapolation theorem ⋮ Weighted fractional Sobolev spaces as interpolation spaces in bounded domains ⋮ Fractional Poincaré and localized Hardy inequalities on metric spaces ⋮ Self-improving Poincaré-Sobolev type functionals in product spaces ⋮ Fractional interpolation inequality and radially symmetric ground states ⋮ An Orlicz-Besov Poincaré inequality via John domains ⋮ A new fractional order Poincare's inequality with weights ⋮ Study of fractional Poincaré inequalities on unbounded domains ⋮ A note on generalized Poincaré-type inequalities with applications to weighted improved Poincaré-type inequalities ⋮ On the interpolation space \((L^p(\Omega), W^{1, p}(\Omega))_{s, p}\) in non-smooth domains ⋮ A fractional Orlicz-Sobolev Poincaré inequality in John domains ⋮ Embedding and compact embedding for weighted and abstract Sobolev spaces ⋮ On the weighted fractional Poincar\'e-type inequalities ⋮ Inverse problems for the fractional-Laplacian with lower order non-local perturbations ⋮ The Bourgain-Brézis-Mironescu formula in arbitrary bounded domains

Cites Work

• Criteria for optimal global integrability of Hajłasz-Sobolev functions
• On fractional Poincaré inequalities
• Sobolev-Poincaré implies John
• Characterizations for fractional Hardy inequality
• On a \((q,p)\)-Poincaré inequality
• On the (\(1,p\))-Poincaré inequality
• On comparability of integral forms
• FRACTIONAL SOBOLEV–POINCARÉ AND FRACTIONAL HARDY INEQUALITIES IN UNBOUNDED JOHN DOMAINS
• Existence for Nonlocal Variational Problems in Peridynamics
• Local approximations and intrinsic characterization of spaces of smooth functions on regular subsets of ℝⁿ
• Fractional Sobolev extension and imbedding
• A Whitney extension theorem in \(L^p\) and Besov spaces
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