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On an inequality of Friedrich's type

Author: Milutin R. Dostanic
Journal: Proc. Amer. Math. Soc. 125 (1997), 2115-2118
MSC (1991): Primary 47A30
MathSciNet review: 1376758
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Abstract: In this paper the dependence of the constant $C$ in the inequality $\int _{G} \left | u \right |^{2} dx \leq C \int _{D} \left | \nabla u \right |^{2}\, dx,\, u{\left .\right |}_{\partial D}=0 $ on simply connected bounded domains $G \subset D \subset R^{2} $ is found.

References [Enhancements On Off] (What's this?)

  • 1. C. Bandle, Isoperimetric inequalities and applications, Pitman, London, 1980. MR 81e:35095
  • 2. R. Courant and D. Hilbert, Methods of Mathematical Physics Vol. 1, Wiley, New York, 1953. MR 16:426a
  • 3. M. Dostanic, The properties of the Cauchy transform on a bounded domain, Journal of Operator Theory (to appear).
  • 4. A. Friedman, Partial differential equations of parabolic type, Prentice Hall, Englewood Cliffs N. Y., 1964. MR 31:6062
  • 5. O. A. Ladyzhenskaya and N. N. Uralt'seva, Linear and Quasilinear elliptic equations, Academic Press, New York, 1969.
  • 6. S. G. Mihlin, Lectures on Mathematical Physics, Moscow, 1968.
  • 7. I.N. Vekua, Generalized analytic functions, Moscow, 1988. MR 90a:30135

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Additional Information

Milutin R. Dostanic
Affiliation: Matematicki Fakultet, Studentski trg 16, Beograd, Serbia

Keywords: Boundary value problems, Cauchy operator
Received by editor(s): November 29, 1995
Received by editor(s) in revised form: February 7, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society

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