This book provides an introduction to elliptic and parabolic equations. While there are numerous monographs focusing separately on each kind of equations, there are very few books treating these two kinds of equations in combination. This book presents the related basic theories and methods to enable readers to appreciate the commonalities between these two kinds of equations as well as contrast the similarities and differences between them.
Chapter 1: Preliminary Knowledge (267 KB)
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- Preliminary Knowledge
- L2 Theory of Linear Elliptic Equations
- L2 Theory of Linear Parabolic Equations
- De Giorgi Iteration and Moser Iteration
- Harnack’s Inequalities
- Schauder’s Estimates for Linear Elliptic Equations
- Schauder’s Estimates for Linear Parabolic Equations
- Existence of Classical Solutions for Linear Equations
- Lp Estimates for Linear Equations and Existence of Strong Solutions
- Fixed Point Method
- Topological Degree Method
- Monotone Method
- Degenerate Equations
Readership: Scholars and graduate students in mathematics, especially, in partial differential equations.
Scholars and graduate students in mathematics, especially, in partial differential equations.