Boundary Value Problems in Complex Analysis

Abstract

The methods of complex variables functions are extensively and effectively employed in the solution of a great variety of mathematical problems that arise in diverse fields of science. For example, the use of analytic functions in many cases yields sufficiently simple methods of solving boundary-value problems for the Laplace equation, to which various problems of hydro-and aerodynamics, the theory of elasticity, electrostatics and so forth reduce. This is due to the close connection between analytic functions of a complex variable and the harmonic functions of two real variables. We will examine certain general problems of the employment of analytic functions in the solution of boundary value problems for the Laplace equation and will give a number of value problems of the solution of problems in physics and mechanics. And a systematic investigation of basic boundary value problem for complex partial differential equations of arbitrary order restricted to model equations.