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On the non-starlikeness of solutions to the starlike interior wake problem

Author(s): Andrew Acker
Journal: Proc. Amer. Math. Soc. 134 (2006), 749-753.
MSC (2000): Primary 35R35, 76B07
Posted: July 18, 2005
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Abstract: We study examples of the starlike interior ``wake problem" for which no starlike solution exists relative to the natural star center of the problem. These examples show that the main result of D.E. Tepper in ``A mathematical model for a wake'' (Michigan Math. J. 31 (1984), 161-165) is not correct.

References:

[A1]
A. ACKER: Heat flow inequalities with application to heat flow optimization problems. SIAM J. Math. Anal 8(1977), pp. 604-618. MR 0473960 (57:13618)

[A2]
A. ACKER: Some free boundary optimization problems and their solutions. Numerische Behandlung von Differentialgleichungen mit besonderer Berucksichtigung freier Randwertaufgaben (J. Albrecht, L. Collatz, G. Hammerlin, editors), Birkhäuser Verlag, Basel 1978, pp. 9-22. (Proceedings of the conference by the same name held at the Mathematisches Forschungsinstitut Oberwolfach, Germany, May 1-7, 1977.) MR 0497989 (80m:35078)

[A3]
A. ACKER: A free boundary optimization problem involving weighted areas, J. Appl. Math. and Phys. (ZAMP) 29 (1978), pp. 395-408. MR 0482457 (58:2524a)

[A4]
A. ACKER: On the qualitative theory of parametrized families of free boundaries. J. reine angew. Math. 193(1989), pp. 134-167. MR 0972364 (90a:35229)

[A5]
A. ACKER: Uniqueness and monotonicity of solutions for the interior Bernoulli free boundary problem in the convex, $n$-dimensional case. Nonlinear Analysis, TMA 13(1988), pp. 1409-1425. MR 1028238 (91a:35168)

[B1]
A. BEURLING: On free boundary problems for the Laplace equation. Seminars on Analytic Functions, Vol. I (1957), pp. 248-263. Institute for Advanced Study, Princeton, N.J.

[B2]
A. BEURLING: The Collected Works of Arne Beurling, Vol. 1. (edited by Carleson, L., Malliavan, P., Neuberger, J., and Werner, J.), Birkhäuser Boston, 1989.MR 1057613 (92k:01046a)

[T1]
D.E. TEPPER: A free boundary problem in the annulus. J. Austral. Math. Soc. (Series A) 34(1983), pp. 177-181. MR 0687323 (84c:31001)

[T2]
D.E. TEPPER: A mathematical model for a wake. Mich. Math. J. 31(1984), pp. 161-165. MR 0752252 (86b:35205)

[T3]
D.E. TEPPER: A jet around an obstacle. In: Topics in Complex Analysis (Proceedings of the special session held at Fairfield, Conn., Oct. 28-29, 1983, D. Shaffer, editor). Contemporary Mathematics series, Vol. 38, American Mathematical Society, 1985, pp. 127-132. MR 0789455

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Additional Information:

Andrew Acker
Affiliation: Department of Mathematics and Statistics, Wichita State University, Wichita, Kansas 67208-0033
Email: acker@math.wichita.edu

DOI: 10.1090/S0002-9939-05-07991-8
PII: S 0002-9939(05)07991-8
Keywords: Ideal fluid, free boundary, geometric constraint, cavitation, starlikeness
Received by editor(s): July 1, 2004
Received by editor(s) in revised form: October 8, 2004
Posted: July 18, 2005
Communicated by: Richard A. Wentworth
Copyright of article: Copyright 2005, American Mathematical Society

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