These lectures concentrate on fundamentals of the modern theory of linear elliptic and parabolic equations in Holder spaces. Krylov 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. This book, with nearly 200 exercises, will provide a good understanding of what kinds of results are available and what kinds of techniques are used to obtain them.

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