On the non-starlikeness of solutions to the starlike interior wake problem
HTML articles powered by AMS MathViewer
- by Andrew Acker PDF
- Proc. Amer. Math. Soc. 134 (2006), 749-753 Request permission
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
- Andrew Acker, Heat flow inequalities with applications to heat flow optimization problems, SIAM J. Math. Anal. 8 (1977), no. 4, 604–618. MR 473960, DOI 10.1137/0508048
- Andrew Acker, Some free boundary optimization problems and their solutions, Numerische Behandlung von Differentialgleichungen mit besonderer Berücksichtigung freier Randwertaufgaben (Tagung Math. Forschungsinst., Oberwolfach, 1977) Internat. Ser. Numer. Math., vol. 39, Birkhäuser, Basel-Boston, Mass., 1978, pp. 9–22. MR 497989
- Andrew Acker, A free boundary optimization problem involving weighted areas, Z. Angew. Math. Phys. 29 (1978), no. 3, 395–408 (English, with German summary). MR 482457, DOI 10.1007/BF01590761
- Andrew Acker, On the qualitative theory of parametrized families of free boundaries, J. Reine Angew. Math. 393 (1989), 134–167. MR 972364
- Andrew Acker, Uniqueness and monotonicity of solutions for the interior Bernoulli free boundary problem in the convex, $n$-dimensional case, Nonlinear Anal. 13 (1989), no. 12, 1409–1425. MR 1028238, DOI 10.1016/0362-546X(89)90102-8
- 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.
- Arne Beurling, The collected works of Arne Beurling. Vol. 1, Contemporary Mathematicians, Birkhäuser Boston, Inc., Boston, MA, 1989. Complex analysis; Edited by L. Carleson, P. Malliavin, J. Neuberger and J. Wermer. MR 1057613
- David E. Tepper, A free boundary problem in an annulus, J. Austral. Math. Soc. Ser. A 34 (1983), no. 2, 177–181. MR 687323, DOI 10.1017/S144678870002320X
- David E. Tepper, A mathematical model for a wake, Michigan Math. J. 31 (1984), no. 2, 161–165. MR 752252, DOI 10.1307/mmj/1029003020
- David E. Tepper, A jet around an obstacle, Topics in complex analysis (Fairfield, Conn., 1983) Contemp. Math., vol. 38, Amer. Math. Soc., Providence, RI, 1985, pp. 127–132. MR 789455, DOI 10.1090/conm/038/16
Additional Information
- Andrew Acker
- Affiliation: Department of Mathematics and Statistics, Wichita State University, Wichita, Kansas 67208-0033
- Email: acker@math.wichita.edu
- Received by editor(s): July 1, 2004
- Received by editor(s) in revised form: October 8, 2004
- Published electronically: July 18, 2005
- Communicated by: Richard A. Wentworth
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 134 (2006), 749-753
- MSC (2000): Primary 35R35, 76B07
- DOI: https://doi.org/10.1090/S0002-9939-05-07991-8
- MathSciNet review: 2180893