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.
General
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