Statements (52)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
partial differential equations
|
| gptkbp:application |
Image Processing
Gravitational Potential Fluid Flow Electrostatic Potential Steady-State Heat Distribution |
| gptkbp:borders |
Dirichlet Boundary Condition
Neumann Boundary Condition |
| gptkbp:category |
Elliptic Partial Differential Equation
|
| gptkbp:dimensions |
Any Dimension
|
| gptkbp:field |
gptkb:Mathematics
gptkb:Physics Engineering |
| gptkbp:firstPublished |
1780s
|
| gptkbp:form |
∇²φ = 0
|
| gptkbp:generalizes |
One-Dimensional Laplace Equation
|
| gptkbp:hasGreenFunction |
Fundamental Solution
|
| gptkbp:hasInvariant |
translator
Rotation Scaling |
| gptkbp:hasSpecialCase |
Poisson Equation
|
| https://www.w3.org/2000/01/rdf-schema#label |
Laplace Equation
|
| gptkbp:involves |
Scalar Field
Second Partial Derivatives |
| gptkbp:involvesOperator |
gptkb:Laplacian
|
| gptkbp:namedAfter |
gptkb:Pierre-Simon_Laplace
|
| gptkbp:notation |
∇²φ = 0
Δφ = 0 |
| gptkbp:order |
gptkb:Second_Order
|
| gptkbp:relatedTo |
gptkb:Laplace_Transform
gptkb:Wave_Equation gptkb:Heat_Equation Helmholtz Equation Poisson Equation Potential Theory |
| gptkbp:solutionCalled |
Harmonic Function
|
| gptkbp:solutionProperty |
Analyticity of Solutions
Maximum Principle Mean Value Property |
| gptkbp:solvedBy |
gptkb:Fourier_Series
Numerical Methods Green's Function Separation of Variables |
| gptkbp:type |
Linear Equation
|
| gptkbp:usedIn |
gptkb:Fluid_Dynamics
Electrostatics Gravitational Potential Theory Heat Conduction |
| gptkbp:variableType |
Scalar Function
|
| gptkbp:bfsParent |
gptkb:Elliptic_Equations
gptkb:Heat_Equation |
| gptkbp:bfsLayer |
8
|