Math 2.0

Potential theory Basic notions Concept

Harmonic function

Builds on Laplacian

Summary

A harmonic function is a twice continuously differentiable function on an open subset of ℝn\mathbb{R}^n whose Laplacian is zero at each point. Harmonic functions describe steady states, such as equilibrium temperatures and electrostatic potentials in empty space.

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Euclidean space, object, no evidence levelEuclidean spaceobjectFunction, concept, no evidence levelFunctionconceptTotal derivative, concept, no evidence levelTotal derivativeconceptFunction of several variables, concept, no evidence levelFunction of several v…conceptVector-valued function, concept, no evidence levelVector-valued functionconceptDifferentiable function of several variables, concept, no evidence levelDifferentiable functi…conceptPartial derivative, concept, no evidence levelPartial derivativeconceptVector field, concept, no evidence levelVector fieldconceptGradient, concept, no evidence levelGradientconceptDivergence, concept, no evidence levelDivergenceconceptLaplacian, concept, no evidence levelLaplacianconceptHarmonic function, concept, no evidence levelHarmonic functionconcept
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Euclidean space object
  2. Function concept
  3. Total derivative concept
  4. Function of several variables concept
  5. Vector-valued function concept
  6. Differentiable function of several variables concept
  7. Partial derivative concept
  8. Vector field concept
  9. Gradient concept
  10. Divergence concept
  11. Laplacian concept
  12. Harmonic function concept

Where this leads

102 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Harmonic_function, lead section
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Aliasessolution-of-laplace-equation
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MSC31B05
UsesLaplacian
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