This book is a rigorous introduction to the abstract theory of partial differential equations. The main prerequisite is familiarity with basic functional analysis: more advanced topics such as Fredholm operators, the Schauder fixed point theorem and Bochner integrals are introduced when needed, and the book begins by introducing the necessary material from the theory of distributions and Sobolev spaces. Using such techniques, the author presents different methods available for solving elliptic, parabolic and hyperbolic equations. He also considers the difference process for the practical...

The theory of boundary value problems for elliptic systems of partial differential equations has many applications in mathematics and the physical sciences. The aim of this book is to "algebraize" the index theory by means of pseudo-differential operators and new methods in the spectral theory of matrix polynomials. This latter theory provides important tools that will enable the student to work efficiently with the principal symbols of the elliptic and boundary operators on the boundary. Because many new methods and results are introduced and used throughout the book, all the theorems are...

Gegenstand dieses Buches sind Randwertaufgaben. Fur elliptische Differentialopera toren werden durch die Bedingung von Lopatinskij-Sapiro ( = covering condition) alle Randwertbedingungen angegeben, die zur normalen Losbarkeit eines Randwertpro blems fuhren. Auch wird die Variationsmethode ausfuhrlich dargelegt und Fragen nach ihrem Verhaltnis zur allgemeinen elliptischen Theorie behandelt. Bei paraboli schen und hyperbolischen Differentialoperatoren werden solche betrachtet, deren rechte Seite (Ableitungen nach x) ein elliptischer Differentialoperator ist, und die Kenntnisse uber elliptische...