Translator Disclaimer
November 2012 The best constant of $L^p$ Sobolev inequality corresponding to Neumann boundary value problem for $(-1)^M(d/dx)^{2M}$
Yorimasa Oshime, Hiroyuki Yamagishi, Kohtaro Watanabe
Hiroshima Math. J. 42(3): 293-299 (November 2012). DOI: 10.32917/hmj/1355238370

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

Download 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

Information

Published: November 2012
First available in Project Euclid: 11 December 2012

zbMATH: 1262.34028
MathSciNet: MR3050123
Digital Object Identifier: 10.32917/hmj/1355238370

Subjects:
Primary: 34B27
Secondary: 46E35

Rights: Copyright © 2012 Hiroshima University, Mathematics Program

JOURNAL ARTICLE
7 PAGES


SHARE
Vol.42 • No. 3 • November 2012
Back to Top