Hitchhiker's guide to the fractional Sobolev spaces

DOI10.1016/j.bulsci.2011.12.004zbMath1252.46023arXiv1104.4345OpenAlexW2011095781MaRDI QIDQ441901

Giampiero Palatucci, Enrico Valdinoci, Eleonora Di Nezza

Publication date: 8 August 2012

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1104.4345

zbMATH Keywords

Sobolev embeddingsfractional Sobolev spacesfractional Laplaciannonlocal energyGagliardo norm

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Fourier integral operators applied to PDEs (35S30)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Local and global minimizers for a variational energy involving a fractional norm
• Density estimates for a variational model driven by the Gagliardo norm
• Traveling waves for a boundary reaction-diffusion equation
• Uniform estimates and limiting arguments for nonlocal minimal surfaces
• Gradient potential estimates
• A duality approach to the fractional Laplacian with measure data
• Nonlinear diffusion of dislocation density and self-similar solutions
• Dirichlet-to-Neumann boundary conditions for multiple scattering problems
• \(\Gamma \)-convergence of some super quadratic functionals with singular weights
• Fractional diffusion limit for collisional kinetic equations
• Slow motion of particle systems as a limit of a reaction-diffusion equation with half-Laplacian in dimension one
• Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in \(n\) variabili
• Proprietà di alcune classi di funzioni in più variabili
• Elliptic PDEs with fibered nonlinearities
• An introduction to Sobolev spaces and interpolation spaces
• Symmetry for a Dirichlet-Neumann problem arising in water waves
• Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
• Energy estimates and 1-D symmetry for nonlinear equations involving the half-Laplacian
• A symmetry result for a general class of divergence form PDEs in fibered media
• Variational problems with free boundaries for the fractional Laplacian
• Fractional Laplacian phase transitions and boundary reactions: a geometric inequality and a symmetry result
• Joint analyticity and analytic continuation of Dirichlet-Neumann operators on doubly perturbed domains
• Relativistic stability of matter. I
• Quasiconformal mappings and extendability of functions in Sobolev spaces
• The spectrum of positive elliptic operators and periodic bicharacteristics
• Nonexistence of simple hyperbolic blow-up for the quasi-geostrophic equation
• Phase transition with the line-tension effect
• The Peierls-Nabarro and Benjamin-Ono equations
• The modulational regime of three-dimensional water waves and the Davey-Stewartson system
• Inverse acoustic and electromagnetic scattering theory.
• Hamiltonian long-wave approximations to the water-wave problem
• The singular set of solutions to non-differentiable elliptic systems
• Elliptic partial differential equations of second order
• Gagliardo-Nirenberg, composition and products in fractional Sobolev spaces
• A two-dimensional model for quasigeostrophic flow: Comparison with the two-dimensional Euler flow
• On the Bourgain, Brezis, and Mironescu theorem concerning limiting embeddings of fractional Sobolev spaces
• Best constants for Sobolev inequalities for higher order fractional derivatives
• Sharp regularity for functionals with (\(p\),\(q\)) growth
• Gravity waves on the surface of the sphere
• A class of integral equations and approximation of \(p\)-Laplace equations
• Dirichlet-to-Neumann map for three-dimensional elastic waves
• Regularity for the nonlinear Signorini problem
• Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian
• The singular set of minima of integral functionals
• Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces
• Théorèmes de trace et d'interpolation. IV
• Rigidity results for elliptic PDEs with uniform limits: an abstract framework with applications
• From the long jump random walk to the fractional Laplacian
• Nonlinear Diffusion with Fractional Laplacian Operators
• Density Estimates for a Nonlocal Variational Model via the Sobolev Inequality
• A nonlocal singular perturbation problem with periodic well potential
• Regularity of the obstacle problem for a fractional power of the laplace operator
• Theory of Sobolev Multipliers
• Embedding theorems for Lipschitz and Lorentz spaces on lower Ahlfors regular sets
• Nonlocal minimal surfaces
• Nonlinear modulation of gravity waves: a rigorous approach
• Weakly Differentiable Functions
• Inequalities in Fourier Analysis on R ⁿ
• Traveling Two and Three Dimensional Capillary Gravity Water Waves
• Financial Modelling with Jump Processes
• Fibered nonlinearities for p(x)-Laplace equations
• An Extension Problem Related to the Fractional Laplacian
• Analyticity of Dirichlet--Neumann Operators on Hölder and Lipschitz Domains
• Fractional Sobolev extension and imbedding
• Layer solutions in a half‐space for boundary reactions
• An integrable normal form for water waves in infinite depth
• Critical nonlinearity exponent and self-similar asymptotics for Lévy conservation laws
• The random walk's guide to anomalous diffusion: A fractional dynamics approach