Local Minimizers of Singularly Perturbed Functionals with Nonlocal Term

By (author) Niko Tzoukmanis

Extent: 154, 154 pages

Publisher: Logos Verlag Berlin

Subjects: Technical Sciences: Computer Science, Engineering, IT, & Math

Series: Augsburger Schriften zur Mathematik, Physik und Informatik

Series volume number: 7

Language: English

(Paperback) (Published)

(August 2004)

ISBN: 9783832506506

5.71 x 8.27 inches

Price: $61.00

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Synopsis
Contributing Authors

Variational problems involving nonlocal terms are of growing importance in the mathematical modeling of microstructures that occur in solid-solid phase transitions. For a model describing an austenite / twinned martensite interface, it is conjectured that the minimizers are highly oscillating near-periodic functions. The nonlocality, however, turns this problem into a very difficult one. In this book, a similar problem is considered. It is given by singularly perturbed functionals including a double-well potential and a quite general nonlocal term with bounded kernel. Using the concept of Gamma-convergence and the Modica-Mortola theorem, the existence of near-periodic local minimizers is shown.

By (author) Niko Tzoukmanis

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