Partial Differential Equations

J. Wloka

doi:10.1017/CBO9781139171755

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 solution of a partial differential equation, emphasising that it is possible to solve them numerically by simple methods. Many examples and exercises are provided throughout, and care is taken to explain difficult points. Advanced undergraduates and graduate students will appreciate this self-contained and practical introduction.

‘The work under discussion is a nice presentation of PDEs and proves to be a valuable source for undergraduate and graduate students at all levels. It highlights the importance of studying diﬀerential equations both in the setting of classical solutions as well as weak solutions.’

Marius Ghergu Source: European Mathematical Society

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Partial Differential Equations

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Contents

Frontmatter
pp i-iv

Contents
pp v-vii

Dedication
pp viii-viii

Preface
pp ix-xii

I - Sobolev spaces
pp 1-138

II - Elliptic differential operators
pp 139-260

III - Strongly elliptic differential operators and the method of variations
pp 261-375

IV - Parabolic differential operators
pp 376-433

V - Hyperbolic differential operators
pp 434-461

VI - Difference processes for the calculation of the solution of the partial differential equation
pp 462-510

References
pp 511-514

Function and distribution spaces
pp 515-515

Index
pp 516-518

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