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Wirtinger-Sobolev Isoperimetric Constants


Constants gamma such that

 [int_Omega|f|^qdx]^(1/q)<=gamma[int_Omegasum_(i=1)^N|(partialf)/(partialx_i)|^pdx]^(1/p),

where f is a real-valued smooth function on a region Omega satisfying some boundary conditions.


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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.

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Wirtinger-Sobolev Isoperimetric Constants

Cite this as:

Weisstein, Eric W. "Wirtinger-Sobolev Isoperimetric Constants." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Wirtinger-SobolevIsoperimetricConstants.html

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