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Selected topics on quadrature domains
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-3125-3030
2007 (English)In: Physica D: Non-linear phenomena, ISSN 0167-2789, Vol. 235, no 02-jan, 90-100 p.Article in journal (Refereed) Published
Abstract [en]

This is a selection of facts, old and recent, about quadrature domains. The text, written in the form of a survey, is addressed to non-experts and covers a variety of phenomena related to quadrature domains, such as: the difference between quadrature domains for subharmonic, harmonic and respectively complex analytic functions, geometric properties of the boundary, instability in the reverse Hele-Shaw flow, dependence and nonuniqueness on the quadrature data, interpretation in terms of function theory on Riemann surfaces, a matrix model and a reconstruction algorithm. Also there are some low degree/order examples where computations can be carried out in detail.

Place, publisher, year, edition, pages
2007. Vol. 235, no 02-jan, 90-100 p.
Keyword [en]
quadrature domain potential, free boundary, Markov moment problem, principal function, hele-shaw flow, dirichlet boundary-problem, 2-dimensional l-problem, integrable structure, moving boundary, 2 dimensions, variational-inequalities, subnormal-operators, extremal solutions, laplacian growth
URN: urn:nbn:se:kth:diva-17107DOI: 10.1016/j.physd.2007.04.015ISI: 000250892200012ScopusID: 2-s2.0-35048895100OAI: diva2:335150
QC 20100525Available from: 2010-08-05 Created: 2010-08-05Bibliographically approved

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