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Elliptic Partial Differential Equations Second Edition [Pehme köide]

  • Formaat: Paperback / softback, 147 pages, kaal: 296 g
  • Sari: Courant Lecture Notes
  • Ilmumisaeg: 30-Apr-2011
  • Kirjastus: American Mathematical Society
  • ISBN-10: 0821853139
  • ISBN-13: 9780821853139
Teised raamatud teemal:
  • Formaat: Paperback / softback, 147 pages, kaal: 296 g
  • Sari: Courant Lecture Notes
  • Ilmumisaeg: 30-Apr-2011
  • Kirjastus: American Mathematical Society
  • ISBN-10: 0821853139
  • ISBN-13: 9780821853139
Teised raamatud teemal:
Lin taught a course at the Courant Institute, New York University, in 1992, and in 1995 Han used and augmented the notes for a course at the University of Notre Dame. They present some basic methods for obtaining various a priori estimates for second-order partial differential equations of the elliptic type, with a particular emphasis on maximal principles, Harnack inequalities, and their applications. Students should have some knowledge of real variables and Sobolev functions. No date is cited for the first edition, but to this second has been added a final chapter on the existence of solutions, primarily the Dirichlet problem for various types of elliptic equations. There is no index. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)
Preface ix
Chapter 1 Harmonic Functions
1(24)
1.1 Guide
1(1)
1.2 Mean Value Properties
1(7)
1.3 Fundamental Solutions
8(7)
1.4 Maximum Principles
15(4)
1.5 Energy Method
19(6)
Chapter 2 Maximum Principles
25(22)
2.1 Guide
25(1)
2.2 Strong Maximum Principle
25(5)
2.3 A Priori Estimates
30(3)
2.4 Gradient Estimates
33(4)
2.5 Alexandroff Maximum Principle
37(7)
2.6 Moving Plane Method
44(3)
Chapter 3 Weak Solutions: Part I
47(20)
3.1 Guide
47(1)
3.2 Growth of Local Integrals
48(7)
3.3 Holder Continuity of Solutions
55(5)
3.4 Holder Continuity of Gradients
60(7)
Chapter 4 Weak Solutions, Part II
67(32)
4.1 Guide
67(1)
4.2 Local Boundedness
67(11)
4.3 Holder Continuity
78(5)
4.4 Moser's Harnack Inequality
83(10)
4.5 Nonlinear Equations
93(6)
Chapter 5 Viscosity Solutions
99(26)
5.1 Guide
99(1)
5.2 Alexandroff Maximum Principle
99(5)
5.3 Harnack Inequality
104(9)
5.4 Schauder Estimates
113(5)
5.5 W2,p Estimates
118(4)
5.6 Global Estimates
122(3)
Chapter 6 Existence of Solutions
125(22)
6.1 Perron Method
125(5)
6.2 Variational Method
130(4)
6.3 Continuity Method
134(2)
6.4 Compactness Methods
136(3)
6.5 Single- and Double-Layer Potentials Methods
139(3)
6.6 Fixed-Point Theorems and Existence Results
142(5)
Bibliography 147
Qing Han, University of Notre Dame, IN.|Fanghua Lin, Courant Institute, New York University, N