Functions of a complex variable Concept
Domain in the complex plane
Summary
A domain in the complex plane is a nonempty open connected subset of , see the definition. Domains are the usual sets on which complex analysis studies holomorphic functions.
Where this leads
23 pages build on this one.
- Green's function for the Laplacian
- Phragmén–Lindelöf principle for subharmonic functions
- Zaremba's punctured ball
- Dirichlet problem
- Maximum principle for subharmonic functions
- Sub-mean value property
- Kakutani's solution of the Dirichlet problem
- Boundary integral method for the Dirichlet problem
- Dirichlet-to-Neumann operator
- Harmonic measure
- Resolutivity of boundary functions
- Bergman space
- Jump relations for layer potentials
- Bergman kernel
- Perron method
- Calderón problem
- Hadamard three-circle theorem for subharmonic functions
- Lindelöf's maximum principle
- Pseudoanalytic function
- Harmonic measure as exit distribution
- Hadamard's two-constants theorem
- Method of fundamental solutions
- Hartogs lemma for subharmonic functions
Further reading
About this page
| Tag | 0EWMDD6C14 |
|---|---|
| URI | m2://0EWMDD6C14 |
| Aliases | region, complex-domain |
| Kind | concept |
| Writing | W0 stub |
| MSC | 30A99 |
| Same as |
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Definitions
Used by
- Green's function for the Laplacian
- Dirichlet problem
- Bergman space
- Bergman kernel
- Pseudoanalytic function