Presents the basic elements of linear partial differential equations in the context of how they are applied to the study of complex analysis. Based on a year-long course at Washington University, requires a grounding in real and complex analysis; also helpful would be some acquaintance with measure theory, and a sophomore-level introductory course in differential equations. Annotation copyright Book News, Inc. Portland, Or.
Ever since the groundbreaking work of J.J. Kohn in the early 1960s, there has been a significant interaction between the theory of partial differential equations and the function theory of several complex variables. Partial Differential Equations and Complex Analysis explores the background and plumbs the depths of this symbiosis.
The book is an excellent introduction to a variety of topics and presents many of the basic elements of linear partial differential equations in the context of how they are applied to the study of complex analysis. The author treats the Dirichlet and Neumann problems for elliptic equations and the related Schauder regularity theory, and examines how those results apply to the boundary regularity of biholomorphic mappings. He studies the ?-Neumann problem, then considers applications to the complex function theory of several variables and to the Bergman projection.
