Small Modifications of Quadrature Domains |
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| Author:
| Morgan, John
Fong, Frederick |
| Series title: | Memoirs of the American Mathematical Society Ser. |
| ISBN: | 978-0-8218-4810-4 |
| Publication Date: | Jun 2010 |
| Publisher: | American Mathematical Society
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| Book Format: | Paperback |
| List Price: | USD $104.00USD $104.00 |
Book Description:
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For a given plane domain, the author adds a constant multiple of the Dirac measure at a point in the domain and makes a new domain called a quadrature domain. The quadrature domain is characterized as a domain such that the integral of a harmonic and integrable function over the domain equals the integral of the function over the given domain plus the integral of the function with respect to the added measure. The family of quadrature domains can be modeled as the Hele-Shaw flow with a...
More DescriptionFor a given plane domain, the author adds a constant multiple of the Dirac measure at a point in the domain and makes a new domain called a quadrature domain. The quadrature domain is characterized as a domain such that the integral of a harmonic and integrable function over the domain equals the integral of the function over the given domain plus the integral of the function with respect to the added measure. The family of quadrature domains can be modeled as the Hele-Shaw flow with a free-boundary problem. The given domain is regarded as the initial domain and the support point of the Dirac measure as the injection point of the flow.