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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.

517.95 --- Differential equations, Partial --- Mathematical analysis --- Functions of complex variables --- Complex variables --- Elliptic functions --- Functions of real variables --- Advanced calculus --- Analysis (Mathematics) --- Algebra --- Partial differential equations --- Differential equations, Partial. --- Functions of complex variables. --- Mathematical analysis. --- 517.1 Mathematical analysis --- 517.95 Partial differential equations --- 517.1. --- 517.1 --- Problèmes aux limites --- Equations aux derivees partielles --- Equations aux derivees partielles elliptiques --- Fonctions de variables complexes --- Problemes aux limites

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517.95 --- 519.6 --- 681.3 *G18 --- Partial differential equations --- Computational mathematics. Numerical analysis. Computer programming --- Partial differential equations: difference methods elliptic equations finite element methods hyperbolic equations method of lines parabolic equations (Numerical analysis) --- 681.3 *G18 Partial differential equations: difference methods elliptic equations finite element methods hyperbolic equations method of lines parabolic equations (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 517.95 Partial differential equations --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Differential equations, Partial --- Numerical solutions. --- Numerical analysis --- Equations aux dérivées partielles --- Analyse numérique --- Equations aux derivees partielles --- Analyse numerique --- Methodes numeriques