Foundations of the Classical Theory of Partial Differential Equations

1. Basic Concepts.- 1. Basic Definitions and Examples.- 2. The Cauchy-Kovalevskaya Theorem and Its Generalizations.- 3. Classification of Linear Differential Equations. Reduction to Canonical Form and Characteristics.- 2. The Classical Theory.- 1. Distributions and Equations with Constant Coefficients.- 2. Elliptic Equations and Boundary-Value Problems.- 3. Sobolev Spaces and Generalized Solutions of Boundary-Value Problems.- 4. Hyperbolic Equations.- 5. Parabolic Equations.- 6. General Evolution Equations.- 7. Exterior Boundary-Value Problems and Scattering Theory.- 8. Spectral Theory of One-Dimensional Differential Operators.- 9. Special Functions.- References.- Author Index.

From the reviews: "...I think the volume is a great success ... a welcome addition to the literature ..." The Mathematical Intelligencer, 1993 "... According to the authors ... the work was written for the nonspecialists and physicists but in my opinion almost every specialist will find something new for herself/himself in the text. ..." Acta Scientiarum Mathematicarum, 1993 "... On the whole, a thorough overview on the classical aspects of the topic may be gained from that volume." Monatshefte für Mathematik, 1993 "... It is comparable in scope with the great Courant-Hilbert Methods of Mathematical Physics, but it is much shorter, more up to date of course, and contains more elaborate analytical machinery...." The Mathematical Gazette, 1993

From the reviews of the first printing, published as volume 30 of the Encyclopaedia of Mathematical Sciences: "... I think the volume is a great success and an excellent preparation for future volumes in the series. ... the introductory style of Egorov and Shubin is .. attractive. ... a welcome addition to the literature and I am looking forward to the appearance of more volumes of the Encyclopedia in the near future. ..."
The Mathematical Intelligencer, 1993
"... According to the authors ... the work was written for nonspecialists and physicists but in my opinion almost every specialist will find something new ... in the text. The style is clear, the notations are chosen luckily. The most characteristic feature of the work is the accurate emphasis on the fundamental notions ..."
Acta Scientiarum Mathematicarum, 1993

"... On the whole, a thorough overview on the classical aspects of the topic may be gained from that volume."
Monatshefte für Mathematik, 1993 "... It is comparable in scope with the great Courant-Hilbert "Methods of Mathematical Physics", but it is much shorter, more up to date of course, and contains more elaborate analytical machinery. A general background in functional analysis is required, but much of the theory is explained from scratch, anad the physical background of the mathematical theory is kept clearly in mind. The book gives a good and readable overview of the subject. ... carefully written, well translated, and well produced."
The Mathematical Gazette, 1993

The book gives an excellent account of the classical part of PDE theory with historical background