This volume contains notes of the lectures given at the Courant Institute and a DMV-Seminar at Oberwolfach. The focus is on the recent work of the authors on semilinear wave equations with critical Sobolev exponents and on wave maps in two space dimensions. Background material and references have been added to make the notes self-contained. The book is suitable for use in a graduate-level course on the topic.

Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

Readership

Graduate students and research mathematicians interested in partial differential equations.

Table of Contents

• The wave equation
• Conservation laws
• Function spaces
• The linear wave equation
• Well-posedness
• Semilinear wave equations
• Wave maps
• Wave maps with symmetry
• Notes
• Bibliography