Partial differential equations. 3rd ed
This new edition is.completely rewritten. Now, the book is divided into 7 chapters entitled as follows: 1. The single first-order equation. 2. Second-order equations: hyperbolic equations for functions of two independent variables. 3. Characteristic manifolds and the Cauchy problem. 4. The Laplace equation. 5. Hyperbolic equations in higher dimensions. 6. Higher-order elliptic equations with constant coefficients. 7. Parabolic equations. As compared with the former edition, an extensive use is made of Fourier transform techniques, Hilbert space, and finite difference methods. Almost all sections contain a subsection with problems. Naturally, the characterization that ``this book still serves as an excellent introduction to partial differential equations'' [see the first edition (1971; Zbl 0209.40001)] is now even more justified. As concerns the spirit of the book, let us quote from the author's Preface to this edition: ``In this book emphasis is put on discovering significant features of a differential equation, and on exploring them as far as possible with a limited amount of machinery from mathematical analysis. Entanglement in a mass of technical details has been avoided, even when this resulted in less general or less complete results''.
higher-order elliptic equations with constant coefficients
scientific article; zbMATH DE number 3663608