Han Q. A Basic Course in Partial Differential Equations

American Mathematical Society, 2011. — 305 p. — (Graduate Studies in Mathematics 120). — ISBN-13 9780821852552.This is a textbook for an introductory graduate course on partial differential equations. Han focuses on linear equations of first and second order. An important feature of his treatment is that the majority of the techniques are applicable more generally. In particular, Han emphasizes a priori estimates throughout the text, even for those equations that can be solved explicitly. Such estimates are indispensable tools for proving the existence and uniqueness of solutions to PDEs, being especially important for nonlinear equations. The estimates are also crucial to establishing properties of the solutions, such as the continuous dependence on parameters.Han's book is suitable for students interested in the mathematical theory of partial differential equations, either as an overview of the subject or as an introduction leading to further study.First-Order Differential Equations
An Overview of Second-Order PDEs
Laplace Equations
Heat Equations
Wave Equations
First-Order Differential Systems
Epilogue