Divergence \& curl with fractional order

DOI10.1016/j.matpur.2022.07.008zbMath1496.35434OpenAlexW4289444653MaRDI QIDQ2166060

Jie Xiao, Li Guang Liu

Publication date: 23 August 2022

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2022.07.008

zbMATH Keywords

ractional-nonlocal pair \(\{(-\Delta)^{\frac{s}{2}},\nabla^s,\operatorname{div}^s,\operatorname{curl}^s\}\)

Mathematics Subject Classification ID

Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Linear first-order PDEs (35F05) Connections of harmonic functions with differential equations in higher dimensions (31B35) Fractional partial differential equations (35R11) Potential operators (47G40)

Related Items (3)

Pointwise decay of solutions to the energy critical nonlinear Schrödinger equations ⋮ Quasilinear Laplace equations and inequalities with fractional orders ⋮ Global endpoint regularity estimates for the fractional Dirichlet problem

Cites Work

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• Calderón-Zygmund operators in Morrey spaces
• Quantitative analysis of two-dimensional flow visualizations using the geometric potential method
• Boundedness of paraproduct operators on RD-spaces
• Morrey spaces in harmonic analysis
• On a new class of fractional partial differential equations
• On the geometry of a steady two dimensional potential flow and its physics
• Some observations on the Green function for the ball in the fractional Laplace framework
• Fractional vector calculus and fractional Maxwell's equations
• Introducing a geometric potential theory for two-dimensional steady flows
• Magnetic Schrödinger operators with compact resolvent
• A note on Riesz potentials
• Geometrical interpretations of continuous and complex-lamellar steady flows
• $Q_\alpha$ analysis on Euclidean spaces
• Fractional div-curl quantities and applications to nonlocal geometric equations
• Compensated compactness and Hardy spaces
• Fractional vector analysis based on invariance requirements (critique of coordinate approaches)
• The fractional variation and the precise representative of \(BV^{\alpha,p}\) functions
• Morrey's fractional integrals in Campanato-Sobolev's space and \(\operatorname{div}F=f\)
• Morrey spaces, their duals and preduals
• A distributional approach to fractional Sobolev spaces and fractional variation: existence of blow-up
• On the product of functions in BMO and H\(^1\)
• A sharp Sobolev trace inequality for the fractional-order derivatives
• On convolution operators leaving \(L^{p,\lambda}\) spaces invariant
• \(H^p\) spaces of several variables
• Fractional Hardy-Sobolev \(L^1\)-embedding per capacity-duality
• On functions of bounded mean oscillation
• Regularity of the obstacle problem for a fractional power of the laplace operator
• Q spaces of several real variables
• Optimal control of the two-dimensional Vlasov-Maxwell system
• Fractional differential operators and divergence equations
• Modern Fourier Analysis
• Fractional Differentiation: Leibniz Meets Hölder
• An Extension Problem Related to the Fractional Laplacian

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