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Analysis Mathematica

, Volume 20, Issue 1, pp 3–10 | Cite as

Notes on best constants in some Sobolev inequalities

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Keywords

Sobolev Inequality Good Constant 
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Замечания о наилучши х константах в некото рых соболевских неравен ствах

Abstract

Мы показываем, что наи лучшие константы в не которых неравенствах для функций из пространс тв Соболева могут быт ь вычислены в терминах решений линейных эллиптичес ких граничных задач. О бсуждается также механизм испол ьзования этих результатов.

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References

  1. [1]
    J. F. Escobar, Sharp constant in a Sobolev trace inequality,Indiana Univ. Math. J.,37(1988), 687–698.CrossRefGoogle Scholar
  2. [2]
    D. Gilbarg andN. Trudinger,Elliptic differential equations of second order, Springer (New York, 1977).Google Scholar
  3. [3]
    W. Han, The best constant in a trace inequality inH 1,Numer. Funct. Anal. Optim.,11(1990), 763–768.Google Scholar
  4. [4]
    W. Han, Quantitative error estimates for material idealization of torsion problems,Math. Comput. Modelling,15(1991), No.9, 47–54.CrossRefGoogle Scholar
  5. [5]
    W. Han, The best constant in a Sobolev inequality,Appl. Anal.,41(1991), 203–208.Google Scholar
  6. [6]
    W. Han, The best constant in a trace inequality,J. Math. Anal. Appl.,163(1992), 512–520.CrossRefGoogle Scholar
  7. [7]
    C. O. Horgan, Eigenvalue estimates and the trace theorem,J. Math. Anal. Appl.,69(1979), 231–242.CrossRefGoogle Scholar
  8. [8]
    C. O. Horgan andL. E. Payne, Lower bounds for free membrane and related eigenvalues,Rend. Mat. Appl., (VII)10(1990), 457–491.Google Scholar
  9. [9]
    J. R.Kuttler and V. G.Sigillito,Estimating eigenvalues with a posteriori/a priori inequalities, Pitman Research Notes in Mathematics Series,135 (London, 1985).Google Scholar
  10. [10]
    V. G.Sigillito,Explicit a priori inequalities with applications to boundary value problems, Pitman Research Notes in Mathematics Series,13 (London, 1977).Google Scholar

Copyright information

© Akadémiai Kiadó 1994

Authors and Affiliations

  • W. Han
    • 1
  1. 1.Department of mathematicsUniversity of iowaIowa cityUSA

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