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Item Details
| Title:
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PARTIAL DIFFERENTIAL EQUATIONS
OVERDETERMINED SYSTEMS DISSIPATIVE SINGULAR SCHRODINGER OPERATOR INDEX THEORY |
| Volume: |
VIII |
| By: |
M.A. Shubin (Editor), Christian Constanda (Trans), P.I. Dudnikov |
| Format: |
Paperback |
| List price:
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£79.99 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
364248946X |
| ISBN 13: |
9783642489464 |
| Publisher: |
SPRINGER-VERLAG BERLIN AND HEIDELBERG GMBH & CO. KG |
| Pub. date: |
14 April, 2012 |
| Edition: |
Softcover reprint of the original 1st ed. 1996 |
| Series: |
Encyclopaedia of Mathematical Sciences 65 |
| Pages: |
268 |
| Synopsis: |
Consider a linear partial differential operator A that maps a vector-valued function Y = (Yl," Ym) into a vector-valued function I = (h,***, II). We assume at first that all the functions, as well as the coefficients of the differen- tial operator, are defined in an open domain Jl in the n-dimensional Euclidean n space IR , and that they are smooth (infinitely differentiable). A is called an overdetermined operator if there is a non-zero differential operator A' such that the composition A' A is the zero operator (and underdetermined if there is a non-zero operator A" such that AA" = 0). If A is overdetermined, then A'I = 0 is a necessary condition for the solvability of the system Ay = I with an unknown vector-valued function y. 3 A simple example in 1R is the operator grad, which maps a scalar func- tion Y into the vector-valued function (8y/8x!, 8y/8x2, 8y/8x3)' A necessary solvability condition for the system grad y = I has the form curl I = O. |
| Illustrations: |
biography |
| Publication: |
Germany |
| Imprint: |
Springer-Verlag Berlin and Heidelberg GmbH & Co. K |
| Returns: |
Returnable |
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