Analysis Mathematica

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

Notes on best constants in some Sobolev inequalities



Sobolev Inequality Good Constant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Замечания о наилучши х константах в некото рых соболевских неравен ствах


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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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

Personalised recommendations