This substantial three-volume work is an upgraded version of the comprehensive qualitative analysis of partial differential equations presented in the earlier edition. The author, assuming that the reader has a basic knowledge of functional analysis and differential geometry, discusses in great detail questions of existence, smoothness, and other properties of solutions of some important classes of equations and systems, linear and nonlinear, arising in a variety of domains in physics and continuum mechanics. The use of Sobolev-type spaces and of the tools provided by distribution theory enhances the depth and breadth of the discussion, adding both power and elegance to it.
Taylor’s book is not for the mathematically faint-hearted, and undergraduates should only touch it if they have read and understood basic material taught in the relevant graduate courses. Graduate students, on the other hand, will find these three volumes to be not just a fine and rigorous treatment of the subject, but also a source of inspiration to apply their knowledge and ability to the solution of other challenging problems in the field of partial differential equations.
In summary, this is an excellent text for all devotees of the charming and thought-provoking byways of higher mathematics.
Christian Constanda is the holder of the Charles W. Oliphant Endowed Chair in Mathematical Sciences at the University of Tulsa, Oklahoma. He is the author, editor, or translator of 22 books, and the author of over 130 peer-reviewed articles. In 2002, his textbook on partial differential equations was selected as an Outstanding Academic Title by the Choice magazine of the American Library Association.