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05/28/2023
Quasi-linear fractional-order operators in Lipschitz domains
We prove Besov boundary regularity for solutions of the homogeneous Diri...
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12/28/2022
Fractional Elliptic Problems on Lipschitz Domains: Regularity and Approximation
This survey hinges on the interplay between regularity and approximation...
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04/14/2022
A deep first-order system least squares method for solving elliptic PDEs
We propose a First-Order System Least Squares (FOSLS) method based on de...
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10/06/2021
Besov regularity for the Dirichlet integral fractional Laplacian in Lipschitz domains
We prove Besov regularity estimates for the solution of the Dirichlet pr...
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09/01/2021
Constructive approximation on graded meshes for the integral fractional Laplacian
We consider the homogeneous Dirichlet problem for the integral fractiona...
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05/13/2021
Finite element algorithms for nonlocal minimal graphs
We discuss computational and qualitative aspects of the fractional Plate...
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03/23/2021
Robust BPX preconditioner for the integral fractional Laplacian on bounded domains
We propose and analyze a robust BPX preconditioner for the integral frac...
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08/13/2020
Finite element approximation of fractional Neumann problems
In this paper we consider approximations of Neumann problems for the int...
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05/07/2020
Local energy estimates for the fractional Laplacian
The integral fractional Laplacian of order s ∈ (0,1) is a nonlocal opera...
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01/09/2020
The Q-tensor Model with Uniaxial Constraint
This chapter is about the modeling of nematic liquid crystals (LCs) and ...
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11/11/2019
A structure-preserving FEM for the uniaxially constrained Q-tensor model of nematic liquid crystals
We consider the one-constant Landau - de Gennes model for nematic liquid...
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06/10/2019