ABSTRACT

Combining both classical and current methods of analysis, this text present discussions on the application of functional analytic methods in partial differential equations. It furnishes a simplified, self-contained proof of Agmon-Douglis-Niremberg's Lp-estimates for boundary value problems, using the theory of singular integrals and the Hilbert transform.

chapter 1|12 pages

Preliminaries

chapter 2|54 pages

Singular Integrals

chapter 3|54 pages

Sobolev Spaces

chapter 4|48 pages

Elliptic Boundary Value Problems

chapter 6|64 pages

Parabolic Evolution Equations

chapter 7|21 pages

Hyperbolic Evolution Equations

chapter 8|67 pages

Retarded Functional Differential Equations