Description
DOVER PUBLICATIONS Kernel Functions And Elliptic Differential Equations In Mathematical Physics by BERGMAN STEFAN ET.AL
This text focuses on the theory of boundary value problems in partial differential equations, which plays a central role in various fields of pure and applied mathematics, theoretical physics, and engineering. Geared toward upper-level undergraduates and graduate students, it discusses a portion of the theory from a unifying point of view and provides a systematic and self-contained introduction to each branch of the applications it employs.The two-part treatment begins with a survey of boundary value problems occurring in certain branches of theoretical physics. It introduces fundamental solutions in a heuristic way and examines their physical significance. Many concepts can be unified by concentrating upon these particular kernels, and the text explains the common mathematical background of widely varying theories, such as those of heat conduction, hydrodynamics, electrostatics, magnetostatics, and elasticity. In addition to its intrinsic interest, this material provides illustrations and exact mathematical formulation of the problems and the methods. The second part is confined to a rather special type of partial differential equation, which is dealt with in the greatest detail so that students can make applications and generalizations to similar problems. PrefaceNote to the ReaderA. Boundary Value Problems for Partial Differential Equations of Elliptic Type1. Theory of Heat Conduction2. Fluid Dynamics3. Electro- and Magnetostatics4. ElasticityB. Kernel Function Methods in the Theory of Boundary Value Problems1. Properties of Solutions2. The Kernel Functions and Their Properties3. Variational and Comparison Theory4. Existence Theory5. Dependence of Kernels on Boundary Conditions and the Differential Equation6. GeneralizationsList of Symbols Used in Part BBibliographyAuthor IndexSubject Index