Statements (42)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:category |
Real-valued functions
Complex-valued functions Potential theory Classical analysis Smooth functions Solutions to elliptic PDEs |
| gptkbp:definedIn |
Twice continuously differentiable functions satisfying Laplace's equation
|
| gptkbp:dimensions |
Defined in any Euclidean space
|
| gptkbp:example |
gptkb:Newtonian_potential
gptkb:Gravitational_potential Electrostatic potential Imaginary part of holomorphic function Real part of holomorphic function |
| gptkbp:field |
gptkb:Mathematics
Analysis Partial Differential Equations |
| gptkbp:generalizes |
Harmonic maps
Polyharmonic functions |
| https://www.w3.org/2000/01/rdf-schema#label |
Harmonic Functions
|
| gptkbp:Laplace's_equation |
Δf = 0
|
| gptkbp:property |
Analytic in open domains
Maximum principle Mean value property |
| gptkbp:relatedTo |
Holomorphic functions
Subharmonic functions Superharmonic functions |
| gptkbp:satisfies |
gptkb:Laplace's_equation
|
| gptkbp:solvedBy |
gptkb:Dirichlet_problem
gptkb:Neumann_problem |
| gptkbp:studiedBy |
gptkb:Carl_Friedrich_Gauss
gptkb:Joseph-Louis_Lagrange gptkb:Pierre-Simon_Laplace gptkb:Simeon_Denis_Poisson |
| gptkbp:usedIn |
gptkb:Physics
gptkb:Gravitation Engineering Electrostatics Fluid dynamics Potential theory |
| gptkbp:bfsParent |
gptkb:Analytic_Functions
|
| gptkbp:bfsLayer |
6
|