Asymptotic behavior of extremals for fractional Sobolev inequalities associated with singular problems

DOI10.1007/s10231-019-00854-9zbMath1427.35318arXiv1807.03449OpenAlexW3101484125MaRDI QIDQ2009076

Yanyan Li

Publication date: 27 November 2019

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.03449

zbMATH Keywords

asymptotic behaviorviscosity solutionsingular problemfractional \(p\)-Laplacian

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Nonlinear elliptic equations (35J60) Viscosity solutions to PDEs (35D40) Fractional partial differential equations (35R11)

Related Items (2)

Mixed local and nonlocal Sobolev inequalities with extremal and associated quasilinear singular elliptic problems ⋮ On the behavior of least energy solutions of a fractional ( p , q ( p ) )-Laplacian problem as p goes to infinity

Cites Work

• Unnamed Item
• Limit problems for a fractional \(p\)-Laplacian as \(p\to\infty\)
• Hitchhiker's guide to the fractional Sobolev spaces
• The fractional Cheeger problem
• Limits as \(p\rightarrow\infty \) of \(p\)-Laplacian problems with a superdiffusive power-type nonlinearity: positive and sign-changing solutions
• On a singular minimizing problem
• The \(\infty\)-eigenvalue problem
• Limit as \(p\to \infty \) of \(p\)-Laplace eigenvalue problems and \(L^\infty \)-inequality of the Poincaré type.
• Limits as \(p \rightarrow \infty \) of \(p\)-Laplacian eigenvalue problems perturbed with a concave or convex term
• A Sobolev non embedding
• Convergence of the eigenvalues of the \(p\)-Laplace operator as \(p\) goes to 1
• Fractional eigenvalues
• Asymptotics for the best Sobolev constants and their extremal functions
• A Hölder infinity Laplacian
• Fractional Sobolev inequalities associated with singular problems
• Limit Branch of Solutions asp → ∞ for a Family of Sub-Diffusive Problems Related to thep-Laplacian
• Some remarks on the measurability of certain sets

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