314 research outputs found
ヒセンケイベッセルホウテイシキニツイテ
京都大学0048新制・論文博士理学博士乙第1953号論理博第379号新制||理||154(附属図書館)3193UT51-47-B470(主査)教授 山口 昌哉, 教授 溝畑 茂, 教授 松浦 重武学位規則第5条第2項該当Kyoto UniversityDA
THE BEST CONSTANT OF L<sup>p</sup> SOBOLEV INEQUALITY CORRESPONDING TO DIRICHLET-NEUMANN BOUNDARY VALUE PROBLEM
We have obtained the best constant of the following Lp
Sobolev inequality
sup
0≤y≤1|
u(j)(y)|
≤C (∫ 01
|
u(M)(x)|
p
dx)1/p
,
where u is a function satisfying u(M) ∈ Lp(0, 1), u(2i)(0) = 0 (0 ≤i ≤
[(M − 1)/2]) and u(2i+1)(1) = 0 (0 ≤ i ≤ [(M − 2)/2]), where u(i) is
the abbreviation of (d/dx)iu(x). In [9], the best constant of the above
inequality was obtained for the case of p = 2 and j = 0. This paper
extends the result of [9] under the conditions p > 1 and 0 ≤ j ≤ M −1.
The best constant is expressed by Bernoulli polynomials
- …