On the limit as \(s\rightarrow 0^+\) of fractional Orlicz-Sobolev spaces

DOI10.1007/S00041-020-09785-ZzbMath1467.46032arXiv2002.05449OpenAlexW3005659427MaRDI QIDQ2218162

Angela Alberico, Andrea Cianchi, Luboš Pick, Lenka Slavíková

Publication date: 14 January 2021

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.05449

zbMATH Keywords

fractional Orlicz-Sobolev spacelimits of smoothness parameters

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Related Items (15)

A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics~II ⋮ Fractional Orlicz-Sobolev embeddings ⋮ Small order asymptotics of the Dirichlet eigenvalue problem for the fractional Laplacian ⋮ A weak-type expression of the Orlicz modular ⋮ Bourgain, Brezis and Mironescu theorem for fractional Sobolev spaces with variable exponents ⋮ Sign-changing solution for a generalized Kirchhoff problem in the fractional Orlicz-Sobolev space with nonsmooth nonlinearity ⋮ On fractional Orlicz‑Sobolev spaces ⋮ A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics. I ⋮ Boundedness of functions in fractional Orlicz-Sobolev spaces ⋮ Maximum principles, Liouville theorem and symmetry results for the fractional \(g\)-Laplacian ⋮ On fractional Orlicz-Sobolev spaces ⋮ On the limit as \(s\to 1^-\) of possibly non-separable fractional Orlicz-Sobolev spaces ⋮ Hardy and Poincaré inequalities in fractional Orlicz-Sobolev spaces ⋮ Neumann and Robin type boundary conditions in Fractional Orlicz-Sobolev spaces ⋮ Maz’ya–Shaposhnikova formula in magnetic fractional Orlicz–Sobolev spaces

Cites Work

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• Hölder inequalities and sharp embeddings in function spaces of \(B_{pq}^ s\) and \(F_{pq}^ s\) type
• Sharp Sobolev type embeddings on the entire Euclidean space
• Limiting embedding theorems for \(W^{s,p}\) when \(s\uparrow 1\) and applications
• On the Bourgain, Brezis, and Mironescu theorem concerning limiting embeddings of fractional Sobolev spaces
• Optimal Orlicz-Sobolev embeddings
• Eigenvalues and minimizers for a non-standard growth non-local operator
• Embedding theorems in the fractional Orlicz-Sobolev space and applications to non-local problems
• Fractional order Orlicz-Sobolev spaces
• Sobolev Spaces

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