This book concentrates on fundamentals of the modern theory of linear elliptic and parabolic equations in Hölder spaces. The author shows that this theory—including some issues of the theory of nonlinear equations—is based on some general and extremely powerful ideas and some simple computations. The main object of study is the first boundary-value problems for elliptic and parabolic equations, with some guidelines concerning other boundary-value problems such as the Neumann or oblique derivative problems or problems involving higher-order elliptic operators acting on the boundary. Numerical approximations are also discussed.

With nearly 200 exercises, this book provides a good understanding of what kinds of results are available and what kinds of techniques are used to obtain them.

Readership

Graduate students and researchers in mathematics, physics, and engineering interested in the theory of partial differential equations.