Constants 
such that
![[int_Omega|f|^qdx]^(1/q)<=gamma[int_Omegasum_(i=1)^N|(partialf)/(partialx_i)|^pdx]^(1/p),](/images/equations/Wirtinger-SobolevIsoperimetricConstants/NumberedEquation1.svg) |
where 
is a real-valued smooth function on a region 
satisfying some boundary
conditions.
Wirtinger-Sobolev Isoperimetric Constants
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References
Finch, S. R. "Sobolev Isoperimetric Constants." §3.6 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 219-225, 2003.Referenced on Wolfram|Alpha
Wirtinger-Sobolev Isoperimetric ConstantsCite this as:
Weisstein, Eric W. "Wirtinger-Sobolev Isoperimetric Constants." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Wirtinger-SobolevIsoperimetricConstants.html