Abstract
The best constant of $L^p$ Sobolev inequality for a function with Neumann boundary condition is obtained. The best constant is expressed by $L^q$ norm of $M$-th order Bernoulli polynomial. For $L^p$ Sobolev inequality, the equality holds for a function which is written by Green function with Neumann boundary value problem for $(-1)^M(d/dx)^{2M}$.
Citation
Yorimasa Oshime. Hiroyuki Yamagishi. Kohtaro Watanabe. "The best constant of $L^p$ Sobolev inequality corresponding to Neumann boundary value problem for $(-1)^M(d/dx)^{2M}$." Hiroshima Math. J. 42 (3) 293 - 299, November 2012. https://doi.org/10.32917/hmj/1355238370
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