A Bourgain-Brezis-Mironescu formula for anisotropic fractional Sobolev spaces and applications to anisotropic fractional differential equations

DOI10.1016/J.JMAA.2022.126805OpenAlexW4307211195WikidataQ115345784 ScholiaQ115345784MaRDI QIDQ2102093

Julián Fernández Bonder, Ignacio Ceresa Dussel

Publication date: 28 November 2022

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

Full work available at URL: https://arxiv.org/abs/2206.11873

zbMATH Keywords

fractional order Sobolev spacesanisotropic Sobolev spacesfractional energies

Mathematics Subject Classification ID

Fractional partial differential equations (35R11) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (3)

Bourgain, Brezis and Mironescu theorem for fractional Sobolev spaces with variable exponents ⋮ Gagliardo representation of norms of ball quasi-Banach function spaces ⋮ Nabla fractional distributed optimization algorithms over undirected/directed graphs

Cites Work

• Unnamed Item
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• Hitchhiker's guide to the fractional Sobolev spaces
• Is a nonlocal diffusion strategy convenient for biological populations in competition?
• Stability of variational eigenvalues for the fractional \(p\)-Laplacian
• Functional analysis, Sobolev spaces and partial differential equations
• Phase segregation dynamics in particle systems with long range interactions. I: Macroscopic limits
• An introduction to \(\Gamma\)-convergence
• Fractional quantum mechanics and Lévy path integrals
• On the Bourgain, Brezis, and Mironescu theorem concerning limiting embeddings of fractional Sobolev spaces
• Gamma convergence and asymptotic behavior for eigenvalues of nonlocal problems
• Stability of solutions for nonlocal problems
• Non-local to local transition for ground states of fractional Schrödinger equations on bounded domains
• Extremal functions for the anisotropic Sobolev inequalities
• Mathematical and Numerical Analysis of Linear Peridynamic Models with Nonlocal Boundary Conditions
• Nonlocal Continuum Field Theories
• Nonlocal Operators with Applications to Image Processing
• Euler Equations, Navier-Stokes Equations and Turbulence
• The Poisson equation from non-local to local
• PRICING OF THE AMERICAN PUT UNDER LÉVY PROCESSES
• Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
• On shape optimization problems involving the fractional laplacian
• The random walk's guide to anomalous diffusion: A fractional dynamics approach
• The concentration-compactness principle for the nonlocal anisotropic \(p\)-Laplacian of mixed order

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