Alberto Bressan; Pierangelo Marcati; Denis Serre; Mark Williams; Kevin Zumbrun Springer-Verlag Berlin and Heidelberg GmbH & Co. KG (2007) Pehmeäkantinen kirja
Luigi Ambrosio; Alberto Bressan; Dirk Helbing; Axel Klar; Enrique Zuazua Springer-Verlag Berlin and Heidelberg GmbH & Co. KG (2012) Pehmeäkantinen kirja
This textbook is addressed to graduate students in mathematics or other disciplines who wish to understand the essential concepts of functional analysis and their applications to partial differential equations.
The book is intentionally concise, presenting all the fundamental concepts and results but omitting the more specialized topics. Enough of the theory of Sobolev spaces and semigroups of linear operators is included as needed to develop significant applications to elliptic, parabolic, and hyperbolic PDEs. Throughout the book, care has been taken to explain the connections between theorems in functional analysis and familiar results of finite-dimensional linear algebra.
The main concepts and ideas used in the proofs are illustrated with a large number of figures. A rich collection of homework problems is included at the end of most chapters. The book is suitable as a text for a one-semester graduate course.
