Fractional elliptic problems on Lipschitz domains: regularity and approximation
DOI10.1007/978-3-031-34089-5_2arXiv2212.14070OpenAlexW4385756698MaRDI QIDQ6191310
Ricardo H. Nochetto, Wenbo Li, Juan Pablo Borthagaray
Publication date: 7 March 2024
Published in: A³N²M: Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2212.14070
Smoothness and regularity of solutions to PDEs (35B65) Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Fractional partial differential equations (35R11)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Nonlocal diffusion and applications
- Efficient and accurate spectral method using generalized Jacobi functions for solving Riesz fractional differential equations
- Higher Sobolev regularity for the fractional \(p\)-Laplace equation in the superquadratic case
- \(\Gamma \)-convergence for nonlocal phase transitions
- Fractional Laplacians on domains, a development of Hörmander's theory of \(\mu\)-transmission pseudodifferential operators
- Graph properties for nonlocal minimal surfaces
- Boundary behavior of nonlocal minimal surfaces
- Global Hölder regularity for the fractional \(p\)-Laplacian
- Interior regularity of solutions of non-local equations in Sobolev and Nikol'skii spaces
- Local elliptic regularity for the Dirichlet fractional Laplacian
- Boundary properties of fractional objects: flexibility of linear equations and rigidity of minimal graphs
- Finite element error estimates for nonlinear elliptic equations of monotone type
- Direct and inverse error estimates for finite elements with mesh refinements
- Regularity results for elliptic equations in Lipschitz domains
- Approximation of sets of finite fractional perimeter by smooth sets and comparison of local and global s-minimal surfaces
- A novel and accurate finite difference method for the fractional Laplacian and the fractional Poisson problem
- A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian
- Numerical approximation of the integral fractional Laplacian
- Higher Hölder regularity for the fractional \(p\)-Laplacian in the superquadratic case
- Localization of the Aronszajn-Slobodeckij norm and application to adaptive boundary element methods. II: The three-dimensional case
- On the Bourgain, Brezis, and Mironescu theorem concerning limiting embeddings of fractional Sobolev spaces
- Adaptive finite element methods with convergence rates
- Space-time adaptive finite elements for nonlocal parabolic variational inequalities
- Accurate numerical methods for two and three dimensional integral fractional Laplacian with applications
- Optimal operator preconditioning for pseudodifferential boundary problems
- Kernel-independent adaptive construction of \(\mathcal{H}^2\)-matrix approximations
- Finite element algorithms for nonlocal minimal graphs
- Nonlocal minimal graphs in the plane are generically sticky
- Fine boundary regularity for the degenerate fractional \(p\)-Laplacian
- What is the fractional Laplacian? A comparative review with new results
- Regularity of the solution to fractional diffusion, advection, reaction equations in weighted Sobolev spaces
- Three representations of the fractional \(p\)-Laplacian: semigroup, extension and Balakrishnan formulas
- Random dispersal vs. non-local dispersal
- Finite element discretizations of nonlocal minimal graphs: Convergence
- Obstacle problems for integro-differential operators: higher regularity of free boundaries
- Spectral approximation of fractional PDEs in image processing and phase field modeling
- \({\mathscr{H}} \)-matrix approximability of inverses of discretizations of the fractional Laplacian
- Adaptive finite element method for fractional differential equations using hierarchical matrices
- Aspects of an adaptive finite element method for the fractional Laplacian: a priori and a posteriori error estimates, efficient implementation and multigrid solver
- Regularity analyses and approximation of nonlocal variational equality and inequality problems
- Nonlocal equations with measure data
- Regularity and Bernstein-type results for nonlocal minimal surfaces
- The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
- Efficient implementation of adaptive P1-FEM in Matlab
- A gradient estimate for nonlocal minimal graphs
- Besov regularity for the Dirichlet integral fractional Laplacian in Lipschitz domains
- Constructive approximation on graded meshes for the integral fractional Laplacian
- Exponential convergence ofhpquadrature for integral operators with Gevrey kernels
- On weighted Poincaré inequalities
- Analysis of the Scott–Zhang interpolation in the fractional order Sobolev spaces
- Primer of Adaptive Finite Element Methods
- Asymptotically Compatible Schemes and Applications to Robust Discretization of Nonlocal Models
- A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations
- Computation of geometric partial differential equations and mean curvature flow
- On the Marchaud-Type Inequality
- Theory of adaptive finite element methods: An introduction
- Nonlocal minimal surfaces
- Interior Estimates for Ritz-Galerkin Methods
- The Conditioning of Boundary Element Equations on Locally Refined Meshes and Preconditioning by Diagonal Scaling
- On a Nonlinear Parabolic Problem Arising in Some Models Related to Turbulent Flows
- On the a posteriori error analysis for equations of prescribed mean curvature
- Localization of the Aronszajn-Slobodeckij norm and application to adaptive boundary elements methods. Part I. The two-dimensional case
- The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion
- Nonlocal Modeling, Analysis, and Computation
- Regularity theory and high order numerical methods for the (1D)-fractional Laplacian
- Regularity of the solution to 1-D fractional order diffusion equations
- Surface Diffusion of Graphs: Variational Formulation, Error Analysis, and Simulation
- SIMILARITY SOLUTIONS IN SOME NON-LINEAR DIFFUSION PROBLEMS AND IN BOUNDARY-LAYER FLOW OF A PSEUDO-PLASTIC FLUID
- Analysis and Approximation of a Fractional Cahn--Hilliard Equation
- Recent progresses in the theory of nonlinear nonlocal problems
- Linear and nonlinear fractional elliptic problems
- Local Energy Estimates for the Fractional Laplacian
- On the stability of Scott-Zhang type operators and application to multilevel preconditioning in fractional diffusion
- Approximation of Integral Fractional Laplacian and Fractional PDEs via sinc-Basis
- Weighted Analytic Regularity for the Integral Fractional Laplacian in Polygons
- A Monotone Discretization for Integral Fractional Laplacian on Bounded Lipschitz Domains: Pointwise Error Estimates under Hölder Regularity
- Local Convergence of the FEM for the Integral Fractional Laplacian
- A Simple Solver for the Fractional Laplacian in Multiple Dimensions
- Fast Fourier-like Mapped Chebyshev Spectral-Galerkin Methods for PDEs with Integral Fractional Laplacian in Unbounded Domains
- Optimal Regularity and Error Estimates of a Spectral Galerkin Method for Fractional Advection-Diffusion-Reaction Equations
- On the Convergence in $H^1$-Norm for the Fractional Laplacian
- Numerical Methods for the Fractional Laplacian: A Finite Difference-Quadrature Approach
- Bootstrap regularity for integro-differential operators and its application to nonlocal minimal surfaces
- The completion of locally refined simplicial partitions created by bisection
- The Mathematical Theory of Finite Element Methods
- EQUATIONS IN CONVOLUTIONS IN A BOUNDED REGION
- Numerical methods for nonlocal and fractional models
- Boundary Element Methods
- Numerical methods for fractional diffusion
- Fractional‐order operators on nonsmooth domains
This page was built for publication: Fractional elliptic problems on Lipschitz domains: regularity and approximation