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2011, Annals of mathematics studies, ISBN 0691151296, Volume no. 177, x, 330
.... The hypoelliptic Laplacian is a family of operators that is supposed to interpolate between the ordinary Laplacian and the geodesic flow... 
Orbit method | Definite integrals | Differential equations, Hypoelliptic | Laplacian operator | Geometry | Analytic | PBMW | Mathematics | Matrices | PBMS | Mathematical Analysis | Hypoelliptic equations | Index theory and related fixed point theorems
Book
IEICE transactions on information and systems, ISSN 0916-8532, 2016, Volume E99.D, Issue 6, pp. 1716 - 1719
Laplacian operator is a basic tool for image processing. For an image with regular pixels, the Laplacian operator can be represented as a stencil... 
spherical camera model | discrete spherical image | Laplacian operator | Discrete Spherical Image | Laplacian Operator | Spherical Camera Model | COMPUTER SCIENCE, SOFTWARE ENGINEERING | COMPUTER SCIENCE, INFORMATION SYSTEMS
Journal Article
IEEE Transactions on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, 05/2007, Volume 29, Issue 5, pp. 886 - 890
Journal Article
Computers & mathematics with applications (1987), ISSN 0898-1221, 2018, Volume 75, Issue 10, pp. 3649 - 3662
In order to address the question of the SPH (Smoothed Particle Hydrodynamics) Laplacian conditioning, a spectral analysis of this discrete operator is performed... 
Eigenvalues | SPH | Conditioning | Laplacian | Spectrum | MATHEMATICS, APPLIED | ALGORITHM | INCOMPRESSIBLE SPH | FLOWS | Mechanics | Mechanics of the fluids | Physics
Journal Article
International journal of geometric methods in modern physics, ISSN 0219-8878, 02/2018, Volume 15, Issue 2
We describe how it is possible to define a Hodge-de Rham Dirac operator associated to a suitable Cartan-Killing metric form upon the exterior algebra over the quantum spheres SUq(2... 
Hodge operators | Quantum spheres | Laplacians | CLIFFORD ALGEBRAS | COVARIANT DIFFERENTIAL CALCULI | SPINORS | PHYSICS, MATHEMATICAL
Journal Article
SIAM journal on mathematical analysis, ISSN 1095-7154, 2019, Volume 51, Issue 1, pp. 197 - 227
We adapt the variational approach to the analysis of first-kind boundary integral equations associated with strongly elliptic partial differential operators from [M. Costabel, SIAM T. Math. Anal., 19 (1988), pp. 613-626] to the (scaled... 
coercive integral equations | first-kind boundary integral equations | MATHEMATICS, APPLIED | FINITE-ELEMENTS | jump relations | Hodge-Laplacian | Maxwell's equations | LIPSCHITZ-DOMAINS | static limit | MAXWELLS EQUATIONS | potential representations | ELEMENT METHODS | TRACES | Numerical Analysis | Analysis of PDEs | Mathematics
Journal Article
Journal of functional analysis, ISSN 0022-1236, 12/2015, Volume 269, Issue 11, pp. 3402 - 3457
On R+d, endowed with the Laguerre probability measure μα, we define a Hodge–Laguerre operator Lα=δδ⁎+δ⁎δ acting on differential forms... 
Riesz transforms | Hodge decomposition | Spectral multipliers | Laguerre polynomials | FUNCTIONAL-CALCULUS | INEQUALITIES | SPACES | EXPANSIONS | ORNSTEIN-UHLENBECK OPERATOR | LAPLACIAN | MATHEMATICS | SEMIGROUPS | RIEMANNIAN VARIETIES | MANIFOLDS | HEAT KERNEL | Derivatives (Financial instruments)
Journal Article
Revista matemática iberoamericana, ISSN 0213-2230, 2013, Volume 29, Issue 3, pp. 1091 - 1126
The purpose of this paper is to derive some Lewy-Stampacchia estimates in some cases of interest, such as the ones driven by non-local operators... 
Integrodifferential operators | Fractional laplacian | Variational inequalities | OBSTACLE PROBLEM | LAPLACIAN | MATHEMATICS | REGULARITY | fractional Laplacian | UNILATERAL PROBLEMS | integrodifferential operators | DEGENERATE ELLIPTIC-EQUATIONS | BOUNDARY
Journal Article
Journal of functional analysis, ISSN 0022-1236, 2012, Volume 262, Issue 5, pp. 2379 - 2402
Two-term Weyl-type asymptotic law for the eigenvalues of the one-dimensional fractional Laplace operator ( − Δ ) α / 2 ( α ∈ ( 0 , 2 ) ) in the interval ( − 1 , 1 ) is given... 
Eigenvalues | Stable process | Fractional Laplacian | Interval | MATHEMATICS | SUBORDINATE PROCESSES | CONTINUITY | CAUCHY PROCESS
Journal Article
International journal of bifurcation and chaos in applied sciences and engineering, ISSN 0218-1274, 2019, Volume 29, Issue 6, p. 1950084
We focus on the structure of the solution set for the nonlinear equation [Formula: see text] where [Formula: see text] and [Formula: see text] are continuous operators... 
homogeneous operator | P-LAPLACIAN | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Monge-Ampere equation | REGULARITY | MULTIDISCIPLINARY SCIENCES | 1ST EIGENVALUE | DIRICHLET PROBLEM | REAL | ELLIPTIC-EQUATIONS | one-sign solution | Global bifurcation
Journal Article
Theoretical computer science, ISSN 0304-3975, 2019, Volume 784, pp. 46 - 64
In spectral graph theory, the Cheeger inequality gives upper and lower bounds of edge expansion in normal graphs in terms of the second eigenvalue of the graph's Laplacian operator... 
Diffusion process | Cheeger's inequality | Directed Hypergraph Laplacian | EIGENVALUES | COMPUTER SCIENCE, THEORY & METHODS | GRAPHS
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 06/2018, Volume 43, Issue 6, pp. 859 - 892
...-Schrödinger operator on domains of containing the singularity 0, where and , the latter being the best constant in the fractional Hardy inequality... 
Critical exponent | nonlocal operators | Hardy inequalities | fractional Laplacian | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | POSITIVE SOLUTIONS | EQUATIONS | SHARP CONSTANTS | SOBOLEV | Operators (mathematics) | Domains | Eigenvalues | Boundary value problems | Linear equations | Analysis of PDEs | Mathematics
Journal Article
Journal of computational physics, ISSN 0021-9991, 2013, Volume 234, Issue 1, pp. 1 - 7
.... The method can be extended to provide discretisations of higher order and for other differential operators, such the gradient, divergence and curl. 
Isotropic Laplacians | Lattice hydrodynamics | Isotropic laplacians | SPINODAL DECOMPOSITION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MODELS | PHYSICS, MATHEMATICAL | Fluid dynamics | Anisotropy | Isotropy | Operators | Computational fluid dynamics | Lattices | Fluid flow | Hydrodynamics | Computational efficiency | Three dimensional
Journal Article
Journal of functional analysis, ISSN 0022-1236, 07/2015, Volume 269, Issue 1, pp. 47 - 79
In this paper, we consider the following problem involving fractional Laplacian operator... 
Infinitely many solutions | Fractional Laplacian | Compactness | Critical elliptic problem | OBSTACLE PROBLEM | MATHEMATICS | EXPONENTS | REGULARITY | BOUNDARY | ELLIPTIC-EQUATIONS | CRITICAL SOBOLEV
Journal Article
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, ISSN 1937-1632, 02/2019, Volume 12, Issue 1, pp. 1 - 26
In the framework of the Laplacian transport, described by a Robin boundary value problem in an exterior domain in R-n, we generalize the definition of the Poincare-Steklov operator to d-set boundaries, n - 2 < d... 
TRACE | MATHEMATICS, APPLIED | INEQUALITIES | SUBSETS | Laplacian transport | Poincare-Steklov operator | d-sets | SOBOLEV SPACES | fractal | LIPSCHITZ-SPACES | ASYMPTOTICS | BOUNDARY | DOMAINS
Journal Article