Potential theoretic study for elliptic partial differential equations
| Project/Area Number |
15K04929
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Hiroshima University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2015-04-01 – 2018-03-31
|
| Project Status |
Completed (Fiscal Year 2017)
|
| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
|
|---|
| Keywords | ソボレフ関数 / 楕円型偏微分方程式 |
|---|
| Outline of Final Research Achievements |
Variable exponent Lebesgue spaces and Sobolev spaces were introduced to discuss nonlinear partial differential equations with non-standard growth condition. These spaces have attracted more and more attention in connection with the study of elasticity and electrorheological fluids. In this research, we studied the boundedness of the Hardy-Littlewood maximal operator on Musielak-Orlicz-Morrey spaces and grand Musielak-Orlicz-Morrey spaces. As an application of the boundedness of the maximal operator, we establish a generalization of Sobolev's inequality, Trudinger's exponential inequality and continuity for Riesz potentials of functions in Musielak-Orlicz-Morrey spaces and grand Musielak-Orlicz-Morrey spaces.
|
Report
(4 results)
Research Products
(26 results)
