Linear Elliptic Equations of Second Order
نویسنده
چکیده
3 4 CONTENTS Preface These lecture notes are intented as an introduction to linear second order elliptic partial differential equations. It can be considered as a continuation of a chapter on elliptic equations of the lecture notes [17] on partial differential equations. In [17] we focused our attention mainly on explicit solutions for standard problems for elliptic, parabolic and hyperbolic equations. The first chapter concerns integral equation methods for boundary value problems of the Laplace equation. This method can be extended to a large class of linear elliptic equations and systems. In the following chapter we consider Perron's method for the Dirichlet problem for the Laplace equation. This method is based on the maximum principle and on an estimates of derivatives of solutions of the Laplace equation. For additional reading we recommend following books: W.
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