| 中文摘要 | 第6-8页 |
| Abstract | 第8-9页 |
| Chapter 1 Preface | 第10-24页 |
| Chapter 2 Regularity of weak solutions of uniformly elliptic andparabolic equations with some critical or supercritical potentials | 第24-56页 |
| 2.1 Introduction | 第24-25页 |
| 2.2 Preliminary | 第25-28页 |
| 2.2.1 Definition of weak solutions | 第25页 |
| 2.2.2 Important special solutions | 第25-28页 |
| 2.3 Laplacian case | 第28-41页 |
| 2.4 A mean value inequality | 第41-45页 |
| 2.5 Variable second order coefficients case | 第45-49页 |
| 2.6 Parabolic case | 第49-56页 |
| Chapter 3 Schauder estimates of the uniformly elliptic equation withan inverse-square potential | 第56-72页 |
| 3.1 Introduction | 第56页 |
| 3.2 Preliminary | 第56-57页 |
| 3.2.1 Definition of weak solutions | 第56-57页 |
| 3.2.2 Two important lemmas | 第57页 |
| 3.3 Equation with constant 2nd order coefficients | 第57-69页 |
| 3.4 Equation with variable coefficients | 第69-72页 |
| Chapter 4 Heat kernel of the operator △-1/r~2 and some applicationsto axially symmetric Navier-Stokes equations | 第72-94页 |
| 4.1 Introduction | 第72-75页 |
| 4.2 Proof of the Theorem 1.0.12 Ⅰ: calculations of the heat kernel | 第75-78页 |
| 4.3 Proof of Corollary 1.0.15 | 第78-80页 |
| 4.4 Proof of the Theorem 1.0.12 Ⅱ: the integral estimates | 第80-86页 |
| 4.5 Proof of Theorem 1.0.18 | 第86-94页 |
| Chapter 5 Appendix | 第94-112页 |
| 5.1 Existence results | 第94-97页 |
| 5.2 Local boundedness of the weak solution and maximum principle | 第97-102页 |
| 5.3 An introduction to the modified Bassel's equation | 第102-104页 |
| 5.4 Weighted L~∞ estimates | 第104-112页 |
| Bibliography | 第112-122页 |
| Acknowledgments | 第122-124页 |
| 个人简历及论文情况 | 第124-125页 |
