Nonlocal self-improving properties: a functional analytic approach

DOI10.2140/tunis.2019.1.151zbMath1409.35043arXiv1707.06294OpenAlexW3100643705MaRDI QIDQ1728151

Moritz Egert, Olli Saari, Simon Bortz, Pascal Auscher

Publication date: 22 February 2019

Published in: Tunisian Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.06294

zbMATH Keywords

maximal regularityfractional differentiabilityanalytic perturbation argumentsCauchy problem for nonlocal parabolic equationslinear nonlocal elliptic equationsnonlocal and stable-like operators

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Abstract parabolic equations (35K90) Fractional derivatives and integrals (26A33) Interpolation between normed linear spaces (46B70) Weak solutions to PDEs (35D30) Fractional partial differential equations (35R11)

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Cites Work

• Unnamed Item
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• Basic estimates for solutions of a class of nonlocal elliptic and parabolic equations
• Nonlinear commutators for the fractional \(p\)-Laplacian and applications
• Meyers inequality and strong stability for stable-like operators
• Hitchhiker's guide to the fractional Sobolev spaces
• Local elliptic regularity for the Dirichlet fractional Laplacian
• Sobolev, Besov and Nikolskii fractional spaces: Imbeddings and comparisons for vector valued spaces on an interval
• Theory of function spaces
• Non-autonomous maximal regularity in Hilbert spaces
• Regularity in \(L_{p}\) Sobolev spaces of solutions to fractional heat equations
• Nonlocal self-improving properties
• J. L. Lions' problem on maximal regularity
• Stability results on interpolation scales of quasi-Banach spaces and applications
• Anisotropic function spaces and related semi–linear hypoelliptic equations

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