This volume is based on PDE courses given by the authors at the Courant Institute and at the University of Notre Dame (IN). Presented are basic methods for obtaining various a priori estimates for second-order equations of elliptic type with particular emphasis on maximal principles, Harnack inequalities, and their applications. The equations considered in the book are linear, however, the presented methods also apply to nonlinear problems. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.
Author(s): Qing Han, Fanghua Lin
Series: Courant lecture notes in mathematics
Publisher: AMS, Courant Institute
Year: 1997
Language: English
Pages: 132
Cover......Page 1
Title page......Page 2
Contents......Page 6
Preface......Page 8
1.2. Mean Value Properties......Page 10
1.3. Fundamental Solutions......Page 17
1.4. Maximum Principles......Page 24
1.5. Energy Method......Page 28
2.2. Strong Maximum Principle......Page 34
2.3. A Priori Estimates......Page 39
2.4. Gradient Estimates......Page 42
2.5. Alexandroff Maximum Principle......Page 46
2.6. Moving Plane Method......Page 52
3.1. Guide......Page 56
3.2. Growth of Local Integrals......Page 57
3.3. Hölder Continuity of Solutions......Page 64
3.4. Hölder Continuity of Gradients......Page 69
4.2. Local Boundedness......Page 76
4.3. Hölder Continuity......Page 87
4.4. Moser's Harnack Inequality......Page 92
4.5. Nonlinear Equations......Page 102
5.2. Alexandroff Maximum Principle......Page 108
5.3. Harnack Inequality......Page 113
5.4. Schauder Estimates......Page 122
5.5. W... Estimates......Page 126
Bibliography......Page 132
