A density property for fractional weighted Sobolev spaces

DOI10.4171/RLM/712zbMath1346.46024arXiv1501.04918MaRDI QIDQ900703

Enrico Valdinoci, Serena Dipierro

Publication date: 22 December 2015

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/1501.04918

zbMATH Keywords

density propertiesweighted fractional Sobolev spaces

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Variational methods applied to PDEs (35A15)

Related Items (24)

Existence of positive solutions for a class of critical fractional Schrödinger equations with potential vanishing at infinity ⋮ Qualitative properties of singular solutions to nonlocal problems ⋮ On density of compactly supported smooth functions in fractional Sobolev spaces ⋮ Existence and nonexistence of solutions to elliptic equations involving the Hardy potential ⋮ Integral representation of solutions using Green function for fractional Hardy equations ⋮ Fractional Sobolev spaces with power weights ⋮ Fractional Hardy equations with critical and supercritical exponents ⋮ Sharp fractional Hardy inequalities with a remainder for \(1 < p < 2\) ⋮ Sharp weighted fractional Hardy inequalities ⋮ Poisson problems involving fractional Hardy operators and measures ⋮ Dirichlet forms and polymer models based on stable processes ⋮ Liouville results for fractional elliptic equations with Hardy potential ⋮ Existence and multiplicity of solutions for Hardy nonlocal fractional elliptic equations involving critical nonlinearities ⋮ Mass and asymptotics associated to fractional Hardy–Schrödinger operators in critical regimes ⋮ Extremals for fractional order Hardy-Sobolev-Maz'ya inequality ⋮ Semilinear mixed problems in exterior domains for \(\sigma \)-evolution equations with friction and coefficients depending on spatial variables ⋮ On density of smooth functions in weighted fractional Sobolev spaces ⋮ Compact Sobolev-Slobodeckij embeddings and positive solutions to fractional Laplacian equations ⋮ Qualitative properties of positive solutions to nonlocal critical problems involving the Hardy-Leray potential ⋮ One-sided fractional derivatives, fractional Laplacians, and weighted Sobolev spaces ⋮ Beyond local maximal operators ⋮ On nonlocal Choquard equations with Hardy-Littlewood-Sobolev critical exponents ⋮ On the decay at infinity of solutions of fractional Schrödinger equations ⋮ Density properties for fractional Sobolev spaces with variable exponents

Cites Work

• Hitchhiker's guide to the fractional Sobolev spaces
• Qualitative properties of positive solutions to nonlocal critical problems involving the Hardy-Leray potential
• Uniqueness of weighted Sobolev spaces with weakly differentiable weights
• Caffarelli-Kohn-Nirenberg type inequalities of fractional order with applications
• Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators
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