Kernel Functions and Elliptic Differential Equations in Mathematical Physics (Repost)
Stefan Bergman, M. Schiffer, "Kernel Functions and Elliptic Differential Equations in Mathematical Physics"
1953 | pages: 446 | ISBN: 012090750X | DJVU | 7,1 mb
1953 | pages: 446 | ISBN: 012090750X | DJVU | 7,1 mb
The subject of this book is the theory of boundary value problems in partial differential equations. This theory plays a central role in various fields of pure and applied mathematics, theoretical physics, and engineering, and has already been dealt with in numerous books and articles. This book discusses a portion of the theory from a unifying point of view. The solution of a partial differential equation of elliptic type is a functional of the boundary values, the coefficients of the differential equation, and the domain considered. The dependence of the solution upon its boundary values has been studied extensively, but its dependence upon the coefficients and upon the domain is almost as important. The problem of the variation of the solution with that of the coefficients of the equation is closely related to questions of stability, which are of decisive importance in many applications. The knowledge of how the solution of a differential equation varies with a change of coefficients or domain permits us to concentrate on the study of simple equations in simple domains and to derive qualitative results from them.
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