Weighted fractional Sobolev spaces as interpolation spaces in bounded domains

DOI10.1002/mana.202200182arXiv2112.03416MaRDI QIDQ6073257

Gabriel Acosta, Irene Drelichman, Ricardo G. Durán

Publication date: 17 October 2023

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.03416

zbMATH Keywords

fractional Sobolev spacesinterpolation spacesirregular domainsGagliardo seminorm

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Interpolation between normed linear spaces (46B70) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (1)

Sharp fractional Hardy inequalities with a remainder for \(1 < p < 2\)

Cites Work

• On fractional Poincaré inequalities
• On improved fractional Sobolev-Poincaré inequalities
• An introduction to Sobolev spaces and interpolation spaces
• Note on Meyers-Serrin's theorem
• On the interpolation space \((L^p(\Omega), W^{1, p}(\Omega))_{s, p}\) in non-smooth domains
• Fractional Sobolev-Poincaré inequalities in irregular domains
• A T(1) theorem for fractional Sobolev spaces on domains
• On comparability of integral forms
• A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations
• Interpolation Theory
• A note on generalized Poincaré-type inequalities with applications to weighted improved Poincaré-type inequalities
• Improved Poincar\'e inequalities in fractional Sobolev spaces
• The Bourgain-Brézis-Mironescu formula in arbitrary bounded domains
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