Download Quadrature domains and their applications: the Harold S. by Peter Ebenfelt, Bjorn Gustafsson, Dmitry Khavinson, Mihai PDF
By Peter Ebenfelt, Bjorn Gustafsson, Dmitry Khavinson, Mihai Putinar
Quadrature domain names have been singled out approximately 30 years in the past via D. Aharonov and H.S. Shapiro in reference to an extremal challenge in functionality idea. on the grounds that then, a chain of coincidental discoveries placed this classification of planar domain names on the heart of crossroads of numerous really self reliant mathematical theories, e.g., strength thought, Riemann surfaces, inverse difficulties, holomorphic partial differential equations, fluid mechanics, operator thought. the amount is dedicated to contemporary advances within the idea of quadrature domain names, illustrating good the multi-facet elements in their nature. The ebook includes a huge selection of open difficulties referring to the final subject matter of quadrature domain names.
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1) Ω holds for all integrable analytic functions f in Ω. This class consists of half-spaces, exteriors of ellipses, exteriors of parabolas and some degenerate cases. See [120] for a complete classification. In higher dimensions there are similar results [40], but they are less complete. , they exactly comprise those initial fluid domains which can be completely emptied by suction at infinity [74], [29], [156]. Null quadrature domains also come up when investigating regularity of free boundaries, namely when finite boundary points to be investigated are “blown up” under scale changes.
Edinburgh Math. Soc. (2) 42 (1999), 433–444. [132] T. Savina, B. Sternin, V. Shatalov, Notes on “mother body” problem in geographics, preprint 1995. ¨ [133] F. Schottky Uber die conforme Abbildung mehrfach zusammenh¨ angender ebener Fl¨ achen, Crelles Journal 83 (1877), 300–351. [134] M. S. Hawley, Half-order differentials on Riemann surfaces, Acta Math. 115 (1966), 199–236. [135] M. C. Spencer, Functionals of Finite Riemann Surfaces, Princeton Univ. Press, Princeton, 1954. [136] H. Analyse Math.
Rep. 24 (1972), 251–258. [117] M. Sakai, A moment problem on Jordan domains, Proc. Amer. Math. Soc. 70 (1978), 35–38. What is a Quadrature Domain? 23 [118] M. Sakai, Analytic functions with finite Dirichlet integrals on Riemann surfaces, Acta Math. 142 (1979), 199–220. [119] M. Sakai, The submeanvalue property of subharmonic functions and its application to the estimation of the Gaussian curvature of the span metric, Hiroshima Math. J. 9 (1979), 555–593 [120] M. Sakai, Null quadrature domains, J.