Geometry In Partial Differential Equations
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-02-1407-4 (ISBN)
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This book emphasizes the interdisciplinary interaction in problems involving geometry and partial differential equations. It provides an attempt to follow certain threads that interconnect various approaches in the geometric applications and influence of partial differential equations. A few such approaches include: Morse-Palais-Smale theory in global variational calculus, general methods to obtain conservation laws for PDEs, structural investigation for the understanding of the meaning of quantum geometry in PDEs, extensions to super PDEs (formulated in the category of supermanifolds) of the geometrical methods just introduced for PDEs and the harmonic theory which proved to be very important especially after the appearance of the Atiyah-Singer index theorem, which provides a link between geometry and topology.
Some applications of the coarea formula to partial differential equations, F. Bethuel and J.M. Ghidaglia; optical Hamiltonian functions, M. Bialy and L. Polterovich; topological obstructions for singular solutions of differential equations, I. Bogaevski and A. Rachimov; minimal surfaces in economic theory, J. Donato; asymptotic expansions in spectral geometry, P.B. Gilkey; s-symmetries of differential equations, D. Gourevitch; deformations and recursion operators for evolution equations, I.S. Krasil'shchik and P.H.M. Kersten; geometric Hamiltonian forms for the Kadomtsev-Petviashvili and Zabolotskaya-Khokhlov equations, B.A. Kupershmidt; singularities, connections and generalized Dirac equations, V. Lychangin and L. Zilbergleit; Hawking's radiation via Fourier integral operators, P.E. Parker; geometry of super PDEs, A. Prastaro; the isoperimetric inequality, Th.M. Rassias; smooth marginal analysis of bifurcation of extremals, Y.I. Sapronov; on the Schrodinger equation for an n-electron atomic, C.S. Sharma; strings and membranes, K.S. Stelle.
| Erscheint lt. Verlag | 1.1.1994 |
|---|---|
| Verlagsort | Singapore |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 981-02-1407-3 / 9810214073 |
| ISBN-13 | 978-981-02-1407-4 / 9789810214074 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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