BOOK
Kernel Functions and Elliptic Differential Equations in Mathematical Physics
This foundational text focuses on the theory of boundary value problems in partial differential equations, a subject central to pure mathematics, engineering, and theoretical physics. Written by two pioneers in the field, the book adopts a unifying point of view by concentrating on specific kernels—particularly the Bergman kernel—to explain the shared mathematical foundations of seemingly disparate physical theories, such as heat conduction, hydrodynamics, electrostatics, and elasticity.
The two-part treatment begins with a survey of physical problems and heuristic solutions before providing a systematic introduction to each branch of its applications. By connecting complex variable theory with physical boundary problems, Bergman and Schiffer transformed abstract geometric properties into powerful, constructive tools for mathematical analysis.
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