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SIAM Journal on Scientific Computing, ISSN 1064-8275, 2018, Volume 40, Issue 4, pp. A2383 - A2405
A numerical scheme is presented for approximating fractional order Poisson problems in two and three dimensions. The scheme is based on reformulating the... 
Numerical approximation | Finite element–spectral method | Fractional laplacian | finite element-spectral method | MATHEMATICS, APPLIED | fractional laplacian | numerical approximation | ELLIPTIC-OPERATORS | EXTENSION PROBLEM | Mathematics - Numerical Analysis | MATHEMATICS AND COMPUTING
Journal Article
Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 04/2016, Volume 36, Issue 4, pp. 1813 - 1845
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 08/2007, Volume 32, Issue 8, pp. 1245 - 1260
The operator square root of the Laplacian (− ▵) 1/2 can be obtained from the harmonic extension problem to the upper half space as the operator that maps the... 
Fractional Laplacian | 35J70 | 26A33 | Degenerate elliptic equations | MATHEMATICS | MATHEMATICS, APPLIED | degenerate elliptic equations | DEGENERATE ELLIPTIC-EQUATIONS | fractional Laplacian | Mathematics - Analysis of PDEs
Journal Article
Advances in Calculus of Variations, ISSN 1864-8258, 10/2016, Volume 9, Issue 4, pp. 323 - 355
We consider the eigenvalue problem for the in an open bounded, possibly disconnected set , under homogeneous Dirichlet boundary conditions. After discussing... 
47J10 | quasilinear nonlocal operators | 35R09 | Nonlocal eigenvalue problems | spectral optimization | 35P30 | Caccioppoli estimates | Quasilinear nonlocal operators | Spectral optimization | MATHEMATICS | MATHEMATICS, APPLIED | SPECTRUM | Eigen values | Functional Analysis | Analysis of PDEs | Mathematics
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 2/2008, Volume 171, Issue 2, pp. 425 - 461
We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle... 
Mathematics, general | Mathematics | MATHEMATICS | DEGENERATE | Studies | Mathematics - Analysis of PDEs
Journal Article
Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 01/2016, Volume 82, pp. 38 - 47
Journal Article
Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, 09/2014, Volume 2014, Issue 9, pp. P09032 - 11
This paper starts by introducing the Grunwald-Letnikov derivative, the Riesz potential and the problem of generalizing the Laplacian. Based on these ideas, the... 
nonlinear dynamics | MECHANICS | PHYSICS, MATHEMATICAL | CALCULUS | Statistical mechanics | Two dimensional | Derivatives
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 08/2019, Volume 390, pp. 306 - 322
Journal Article
Proceedings of the Royal Society of Edinburgh Section A: Mathematics, ISSN 0308-2105, 2019, Volume 149, Issue 5, pp. 1 - 18
We give a unified approach to strong maximum principles for a large class of nonlocal operators of order s is an element of (0, 1) that includes the Dirichlet,... 
maximum principle | Fractional Laplace operators | MATHEMATICS | MATHEMATICS, APPLIED | OPERATOR | REGULARITY | ELLIPTIC-EQUATIONS | Dirichlet problem | Principles
Journal Article
Mathematics and Computers in Simulation, ISSN 0378-4754, 02/2020, Volume 168, pp. 122 - 134
Journal Article
Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 2013, Volume 208, Issue 1, pp. 109 - 161
In this work we establish trace Hardy and trace Hardy-Sobolev-Maz'ya inequalities with best Hardy constants for domains satisfying suitable geometric... 
MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | CONSTANT | GAMMA-CONVERGENCE | HALF-SPACE | CENSORED STABLE PROCESSES | DOMAINS | Half spaces | Exponents | Mathematical analysis | Inequalities | Series (mathematics) | Constants | Convexity | Archives
Journal Article
Annales de l'Institut Henri Poincaré / Analyse non linéaire, ISSN 0294-1449, 03/2017, Volume 34, Issue 2, pp. 439 - 467
We present a construction of harmonic functions on bounded domains for the spectral fractional Laplacian operator and we classify them in terms of their... 
Large solutions | Dirichlet problem | Spectral fractional Laplacian | Boundary blow-up solutions | MATHEMATICS, APPLIED | BEHAVIOR | REGULARITY | DIRICHLET LAPLACIANS | ELLIPTIC-EQUATIONS | HEAT KERNEL | KILLED BROWNIAN-MOTION | GREEN-FUNCTION | OPERATORS | DOMAINS | Analysis of PDEs | Mathematics
Journal Article
Acta Physica Polonica B, ISSN 0587-4254, 05/2018, Volume 49, Issue 5, pp. 921 - 942
We address Levy-stable stochastic processes in bounded domains, with a focus on a discrimination between inequivalent proposals for what a boundary... 
BROWNIAN-MOTION | EIGENVALUES | STATES | PHYSICS, MULTIDISCIPLINARY | TIME | EIGENFUNCTIONS | SPECTRAL PROPERTIES
Journal Article
SIAM Journal on Scientific Computing, ISSN 1064-8275, 2017, Volume 39, Issue 4, pp. A1320 - A1344
Journal Article
Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 10/2015, Volume 35, Issue 10, pp. 4905 - 4929
We show that the fractional Laplacian can be viewed as a Dirichlet-to-Neumann map for a degenerate hyperbolic problem, namely, the wave equation with an... 
Wave equation | Oscillatory integrals | Schrödinger group | Fractional Laplacian | Bessel functions | MATHEMATICS | MATHEMATICS, APPLIED | wave equation | oscillatory integrals | Schrodinger group | OPERATORS
Journal Article
Computational Mathematics and Mathematical Physics, ISSN 0965-5425, 03/2017, Volume 57, Issue 3, pp. 373 - 386
In this paper we study obstacle problems for the Navier (spectral) fractional Laplacian (-Delta(Omega)) (s) of order s is an element of (0,1) in a bounded... 
free boundary problems | spectral fractional Laplacian | Variational inequalities | OBSTACLE PROBLEM | MATHEMATICS, APPLIED | REGULARITY | EQUATIONS | PHYSICS, MATHEMATICAL | OPERATORS | EXTENSION PROBLEM | Studies | Boundary value problems | Mathematical models | Mathematics | Obstacles | Spectra | Computation | Inequalities | Fluid flow | Mathematics - Analysis of PDEs
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 9/2011, Volume 42, Issue 1, pp. 21 - 41
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 05/2020, Volume 40, Issue 2, pp. 585 - 600
We consider Laplacian fractional revival between two vertices of a graph . Assume that it occurs at time between vertices 1 and 2. We prove that for the... 
spectral decomposition | 05C50 | 81P45 | quantum information transfer | Laplacian matrix | fractional revival | 15A18 | MATHEMATICS | PERFECT STATE TRANSFER
Journal Article
Advances in Difference Equations, ISSN 1687-1839, 12/2013, Volume 2013, Issue 1, pp. 1 - 12
In this paper, we study the p-Laplacian model involving the Caputo fractional derivative with Dirichlet-Neumann boundary conditions. Using a fixed point... 
Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | Mathematics | Partial Differential Equations | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | BOUNDARY-VALUE-PROBLEMS | DIFFERENTIAL-EQUATIONS | POINTS
Journal Article
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