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^p 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

On the Radius of Convergence of the Simplest Power Series Solution of Painleve-I equation II(A Singular Solution)

In our previous paper [1] we considered the simplest power series solution of the Painleve-I equation which is regular at the origin. This note is a sequel to it. Here we consider another simplest Laurent series solution which is singular at the origin. Important feature of this solution is the location of the singularities. The location of the nearest singularity from the origin is given by the radius S of convergence of this Laurent series. The value of S is calculated numerically by the same method as in [1]. We obtained S = 2.56.... Various theoretical bounds for S are also obtained. The mathematical part of this work was done by Kametaka and the numerical part by Noda

Positivity and Hierarchical Structure of four Green Functions Corresponding to a Bending Problem of a Beam on a half line

We consider the boundary value problem for fourth order linear ordinary differential equation in a half line (0,∞), which represents bending of a beam on an elastic foundation under a tension. A tension is relatively stronger than a spring constant of elastic foundation. We here treat four self-adjoint boundary conditions, clamped, Dirichlet, Neumann and free edges, at x = 0. We show the positivity and the hierarchical structure of four Green functions