2016 Fiscal Year Final Research Report
Best evaluation of the Sobolev inequality using the reproducing kernel theory and its applications
| Project/Area Number |
25400210
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Foundations of mathematics/Applied mathematics
|
|---|
| Research Institution | Nihon University |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
NAGAI Atsushi 日本大学, 生産工学部, 教授 (90304039)
|
|---|
| Project Period (FY) |
2013-04-01 – 2017-03-31
|
| Keywords | ソボレフ不等式 / 最良定数 |
|---|
| Outline of Final Research Achievements |
The subject of this research is to obtain best evaluation of a Sobolev inequality. In continuous version, we have treated of Thomson cable (a continuous model) and a free boundary value problem for a 2M-th order operator (no lower terms). In discrete version, we have treated the Mobius ladder, C60 fullerene buckyball, the truncated regular M-hedron (M=4,6,8) and the Toeplitz graph. In each case, we have computed a best constant and family of best functions for the Sobolev inequality. These are important results to become the clue in studying the future Sobolev inequality.
|
| Free Research Field |
微分方程式論
|
