About: Laplace operator

Property	Value
dbo:description	Divergenz des Gradienten (de) אופרטור דיפרנציאלי באנליזה וקטורית (iw) opérateur différentiel appliqué à un champ scalaire (fr) duagrada diferenciala operatoro; la spuro de la Hess-matrico (eo) operador diferencial, representación en otros sistemas coordenados y propiedades (es) divergence gradientu (cs) divergence of the gradient (en) operator różniczkowy drugiego rzędu (pl) operatore matematico (it) مؤثر تفاضلي عبارة عن تركيب مؤثري التباعد والتدرج (ar)
dbo:wikiPageExternalLink	http://ramanujan.math.trinity.edu/rdaileda/teach/s12/m3357/lectures/lecture_3_27_2_short.pdf https://feynmanlectures.caltech.edu/II_12.html http://farside.ph.utexas.edu/teaching/em/lectures/node23.html https://link.springer.com/article/10.1140/epjs/s11734-021-00317-4,Laplace https://www.genealogy.math.ndsu.nodak.edu/id.php%3Fid=59087
dbo:wikiPageWikiLink	dbr:List_of_formulas_in_Riemannian_geometry dbr:Unit_sphere dbr:Maxwell's_equations dbr:Rotation dbr:Metric_tensor dbc:Fourier_analysis dbr:Harmonic_function dbr:Blob_detection dbr:Laplacian_of_Gaussian dbr:Curvilinear_coordinates dbr:Laplace–Beltrami_operator dbr:Vacuum dbr:Velocity dbr:Zenith_angle dbr:Vector_field dbr:Diffusion dbr:Schrödinger_equation dbr:Riemannian_manifold dbr:Scale_space dbr:Trace_(linear_algebra) dbr:Computer_vision dbr:Spectral_theory dbr:Discrete_Laplace_operator dbr:Vector_Laplacian dbr:Klein–Gordon_equation dbr:Differential_operator dbr:Earnshaw's_theorem dbr:Spherical_harmonics dbr:Hodge_star_operator dbr:Orthonormal_basis dbr:Del_in_cylindrical_and_spherical_coordinates dbr:Hermann_Weyl dbc:Differential_operators dbr:Del dbr:Eigenfunction dbr:Laplace_operators_in_differential_geometry dbr:Stationary_point dbr:Mathematics dbr:Physics dbr:Quantum_mechanics dbr:N-sphere dbr:Scalar_field dbr:Wave_equation dbr:Open_set dbr:Heat_equation dbr:Hessian_matrix dbr:Hodge_theory dbr:Scalar_(mathematics) dbr:Functional_(mathematics) dbr:Colatitude dbr:Cartesian_coordinate_system dbr:Euclidean_space dbr:Particle_physics dbr:Spectral_theorem dbr:Viscosity dbr:Elliptic_operator dbr:Reflection_(mathematics) dbr:Divergence dbr:Eigenvalue dbr:Hilbert_space dbr:Partial_derivative dbr:Rellich–Kondrachov_theorem dbr:Mass_distribution dbr:Natural_units dbr:Orthogonal_transformation dbr:Orthonormal dbr:Second-order_differential_equation dbc:Pierre-Simon_Laplace dbc:Elliptic_partial_differential_equations dbc:Harmonic_functions dbr:Divergence_theorem dbr:Laplace's_equation dbr:Self-adjoint_operator dbr:Tensor_field dbr:Real-valued_function dbr:Minkowski_space dbr:D'Alembert_operator dbr:Weyl's_lemma_(Laplace_equation) dbr:Compact_operator dbr:Differential_form dbr:Christoffel_symbols dbr:Incompressible_flow dbr:Analysis_on_fractals dbr:Dirichlet_form dbr:Discrete_exterior_calculus dbr:Covariant_derivative dbr:Fluid_mechanics dbr:Gauss's_law dbr:Gradient dbr:Celestial_mechanics dbr:Edge_detection dbr:Pseudo-Riemannian_manifold dbr:Homogeneous_function dbr:Helmholtz_equation dbc:Linear_operators_in_calculus dbc:Multivariable_calculus dbr:Derivative dbr:Lp_space dbr:Electric_potential dbr:Newtonian_fluid dbr:Dirichlet_energy dbr:Gravitational_potential dbr:Poisson's_equation dbr:Exterior_derivative dbr:Poincaré_inequality dbr:De_Rham_cohomology dbr:Weitzenböck_identity dbr:Isometry_group dbr:Spherical_coordinates dbr:Diffusion_equation dbr:Einstein_summation_convention dbr:Independent_variable dbr:Del_squared_(disambiguation) dbr:Differential_equations dbr:Polar_coordinates dbr:Jacobian_matrix dbr:Image_processing dbr:Cartesian_coordinates dbr:N_sphere dbr:Electric_constant dbr:Electrostatic_potential dbr:Pierre-Simon_de_Laplace dbr:Time_scale_calculus dbr:Stress_(physics) dbr:Green's_first_identity dbr:Mathematical_operator dbr:Fundamental_lemma_of_calculus_of_variations dbr:Azimuthal_angle dbr:Continuously_differentiable dbr:Coordinate_systems dbr:Charge_distribution dbr:D'Alembertian dbr:Navier-Stokes_equations dbr:Net_flux dbr:Cylindrical_coordinates dbr:Hyperbolic_operator dbr:Diffusion_equilibrium dbr:Ultrahyperbolic_operator dbr:Unit_normal dbr:Codifferential dbr:Laplacian dbr:Cartesian_coordinate dbr:Euclidean_transformation dbr:Non-Euclidean dbr:Infinitely_differentiable dbr:Translation_(mathematics) dbr:Vector_triple_product
dbp:id	p/l057510 (en)
dbp:title	Laplace operator (en) Laplacian (en)
dbp:urlname	Laplacian (en)
dbp:wikiPageUsesTemplate	dbt:Authority_control dbt:Calculus dbt:Reflist dbt:Math dbt:See_also dbt:Citation dbt:About dbt:MathWorld dbt:Calculus_topics dbt:Mvar dbt:Main_article dbt:NumBlk dbt:Springer dbt:I_sup dbt:EqRef dbt:Short_description
dct:subject	dbc:Fourier_analysis dbc:Differential_operators dbc:Pierre-Simon_Laplace dbc:Elliptic_partial_differential_equations dbc:Harmonic_functions dbc:Linear_operators_in_calculus dbc:Multivariable_calculus
gold:hypernym	dbr:Operator
rdfs:label	Laplace operator (en) Operador laplacià (ca) مؤثر لابلاس (ar) Laplaceův operátor (cs) Laplaca operatoro (eo) Operador laplaciano (es) Laplace-Operator (de) Opérateur laplacien (fr) Operatore di Laplace (it) ラプラス作用素 (ja) Laplace-operator (nl) 라플라스 연산자 (ko) Laplaciano (pt) Operator Laplace’a (pl) Оператор Лапласа (uk) Оператор Лапласа (ru) Laplaceoperatorn (sv) 拉普拉斯算子 (zh)
rdfs:seeAlso	dbr:Cylinder dbr:Hearing_the_shape_of_a_drum dbr:Spherical_coordinate_system dbr:Del
owl:sameAs	yago-res:Laplace operator http://d-nb.info/gnd/4166772-4 freebase:Laplace operator wikidata:Laplace operator dbpedia-it:Laplace operator dbpedia-nl:Laplace operator dbpedia-de:Laplace operator dbpedia-fr:Laplace operator dbpedia-tr:Laplace operator dbpedia-zh:Laplace operator dbpedia-ja:Laplace operator dbpedia-pt:Laplace operator dbpedia-he:Laplace operator dbpedia-ro:Laplace operator dbpedia-da:Laplace operator dbpedia-es:Laplace operator dbpedia-hu:Laplace operator dbpedia-fa:Laplace operator dbpedia-ru:Laplace operator dbpedia-sv:Laplace operator dbpedia-vi:Laplace operator dbpedia-pl:Laplace operator dbpedia-ko:Laplace operator dbpedia-be:Laplace operator dbpedia-et:Laplace operator dbpedia-ca:Laplace operator dbpedia-ar:Laplace operator dbpedia-bg:Laplace operator dbpedia-cs:Laplace operator dbpedia-cv:Laplace operator dbpedia-eo:Laplace operator dbpedia-gl:Laplace operator dbpedia-hy:Laplace operator dbpedia-io:Laplace operator dbpedia-is:Laplace operator dbpedia-kk:Laplace operator dbpedia-lt:Laplace operator dbpedia-nn:Laplace operator dbpedia-no:Laplace operator dbpedia-pms:Laplace operator dbpedia-sh:Laplace operator dbpedia-simple:Laplace operator dbpedia-sk:Laplace operator dbpedia-sl:Laplace operator dbpedia-sr:Laplace operator dbpedia-uk:Laplace operator dbpedia-global:Laplace operator dbr:Laplace operator
prov:wasDerivedFrom	wikipedia-en:Laplace_operator?oldid=1289360118&ns=0
foaf:isPrimaryTopicOf	wikipedia-en:Laplace_operator
is dbo:knownFor of	dbr:Pierre-Simon_Laplace
is dbo:wikiPageDisambiguates of	dbr:Laplace_(disambiguation)
is dbo:wikiPageRedirects of	dbr:Vector_Laplacian dbr:Hodge-Laplace_operator dbr:Hodge-Laplacian dbr:Hodge_Laplacian dbr:Del-squared dbr:Spherical_Laplacian dbr:Laplace's_differential_equation dbr:Laplacian dbr:Laplacian_operator dbr:Grad_squared dbr:∇² dbr:Vector_laplacian
is dbo:wikiPageWikiLink of	dbr:Finite_difference_method dbr:Kähler_identities dbr:Martingale_(probability_theory) dbr:Integration_by_parts dbr:Partial_differential_equation dbr:Stokes'_law dbr:Gaussian_curvature dbr:Scale-invariant_feature_transform dbr:Parabolic_partial_differential_equation dbr:Parametrix dbr:Lane–Emden_equation dbr:List_of_mathematical_symbols_by_subject dbr:Harmonic_function dbr:Rotational_invariance dbr:Laplace–Beltrami_operator dbr:Vector_calculus_identities dbr:Allee_effect dbr:∆ dbr:Diffusion dbr:Schrödinger_equation dbr:Stochastic_processes_and_boundary_value_problems dbr:Green's_function dbr:Poincaré_metric dbr:Discrete_Laplace_operator dbr:Prewitt_operator dbr:Vector_Laplacian dbr:André_Lichnerowicz dbr:Klein–Gordon_equation dbr:Differential_operator dbr:Hodge_star_operator dbr:Bounded_operator dbr:Alexandru_Proca dbr:Del_in_cylindrical_and_spherical_coordinates dbr:Del dbr:Laplace_(disambiguation) dbr:Delta dbr:Neumann_boundary_condition dbr:Laplace_operators_in_differential_geometry dbr:History_of_mathematical_notation dbr:Heat_kernel dbr:Bessel_potential dbr:Phase-contrast_X-ray_imaging dbr:Continuity_equation dbr:Acoustic_wave_equation dbr:Eigendecomposition_of_a_matrix dbr:Inhomogeneous_electromagnetic_wave_equation dbr:Wave_equation dbr:Velocity_potential dbr:Fractional_calculus dbr:Heat_equation dbr:Sobolev_space dbr:Ornstein–Uhlenbeck_operator dbr:Isospectral dbr:Itô_diffusion dbr:Angular_momentum_operator dbr:Dirichlet_boundary_condition dbr:Ricci_curvature dbr:Cold-air_damming dbr:Greek_letters_used_in_mathematics,_science,_and_engineering dbr:Green's_function_for_the_three-variable_Laplace_equation dbr:Green_measure dbr:Riesz_potential dbr:Boggio's_formula dbr:Earth's_magnetic_field dbr:List_of_common_physics_notations dbr:Brownian_motion dbr:Fourier_optics dbr:Spectral_geometry dbr:Gårding's_inequality dbr:Tidal_tensor dbr:Curve-shortening_flow dbr:Delta_(letter) dbr:Elliptic_operator dbr:Hilbert_space dbr:Manifold dbr:Pólya–Szegő_inequality dbr:Vorticity_equation dbr:Pierre-Simon_Laplace dbr:Laplace's_equation dbr:Diffraction dbr:Hankel_transform dbr:D'Alembert_operator dbr:Halbach_array dbr:Molecular_Hamiltonian dbr:Polyharmonic_spline dbr:Novikov–Shubin_invariant dbr:Weyl's_lemma_(Laplace_equation) dbr:Weyl_metrics dbr:Fourier_series dbr:Nuclear_shell_model dbr:Lone_pair dbr:List_of_unsolved_problems_in_mathematics dbr:Relativistic_heat_conduction dbr:Gaussian_blur dbr:List_of_French_inventions_and_discoveries dbr:Screened_Poisson_equation dbr:Discrete_Poisson_equation dbr:Distorted_Schwarzschild_metric dbr:List_of_partial_differential_equation_topics dbr:P-Laplacian dbr:Open-channel_flow dbr:Infinitesimal_generator_(stochastic_processes) dbr:Harmonic_conjugate dbr:Harmonic_coordinate_condition dbr:Staggered_fermion dbr:List_of_Fourier_analysis_topics dbr:Multilinear_polynomial dbr:Generalizations_of_the_derivative dbr:Helmholtz_equation dbr:Del_squared dbr:Rayleigh–Faber–Krahn_inequality dbr:Conformastatic_spacetimes dbr:Glossary_of_mathematical_symbols dbr:Vector_calculus dbr:Laplacian_of_the_indicator dbr:Gravitational_potential dbr:Green's_identities dbr:Potential_flow dbr:Poisson's_equation dbr:Lions–Lax–Milgram_theorem dbr:Oscillatory_integral dbr:Oseen_equations dbr:Liouville's_equation dbr:Horn–Schunck_method dbr:Hydrogen_atom dbr:List_of_scientific_laws_named_after_people dbr:Luke's_variational_principle dbr:Maps_of_manifolds dbr:Slowly_varying_envelope_approximation dbr:Poincaré_inequality dbr:Dissipative_operator dbr:Limiting_absorption_principle dbr:Real_analytic_Eisenstein_series dbr:Harmonic_Maass_form dbr:Elliptic_boundary_value_problem dbr:Geometry_processing dbr:Mild-slope_equation dbr:Poisson_wavelet dbr:Quantum_graph dbr:Energy_cascade dbr:Multi-focus_image_fusion dbr:PDE-constrained_optimization dbr:Tamper_(nuclear_weapon) dbr:Selberg's_1/4_conjecture dbr:Vector_spherical_harmonics dbr:Kazhdan's_property_(T) dbr:Exterior_calculus_identities dbr:Trigonometric_Rosen–Morse_potential dbr:Margaret_Rayner dbr:Naoki_Saito_(mathematician) dbr:Viscosity_solution dbr:Minakshisundaram–Pleijel_zeta_function dbr:Chern's_conjecture_for_hypersurfaces_in_spheres dbr:Sylvestre_Gallot dbr:Glossary_of_string_theory dbr:List_of_things_named_after_Pierre-Simon_Laplace dbr:Dirac_equation_in_curved_spacetime dbr:Kuramoto–Sivashinsky_equation dbr:Hodge-Laplace_operator dbr:Hodge-Laplacian dbr:Hodge_Laplacian dbr:List_of_letters_used_in_mathematics_and_science dbr:Del-squared dbr:Spherical_Laplacian dbr:Laplace's_differential_equation dbr:Laplacian dbr:Laplacian_operator dbr:Grad_squared dbr:∇² dbr:Vector_laplacian
is dbp:knownFor of	dbr:Pierre-Simon_Laplace
is foaf:primaryTopic of	wikipedia-en:Laplace_operator