Open AccessThe best constant of Sobolev inequality corresponding to anti-periodic boundary value problem
Author(s) -
Jozef Kiseľák
Publication year - 2014
Publication title -
electronic journal of qualitative theory of differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.524
H-Index - 33
ISSN - 1417-3875
DOI - 10.14232/ejqtde.2014.1.62
Subject(s) - mathematics , constant (computer programming) , sobolev space , mathematical analysis , boundary value problem , value (mathematics) , inequality , sobolev inequality , boundary (topology) , pure mathematics , statistics , computer science , programming language
In this paper we establish the best constant of Lp Sobolev inequality for a function with anti-periodic boundary conditions. The best constant is expressed by Lq norm of (M − 1)-th order Euler polynomial. Lyapunov-type inequality for certain higher order differential equation including 1-dim p-Laplacian is obtained by the usage of this constant.
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