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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Local Minimizers of Singularly Perturbed Functionals with Nonlocal Term

Local Minimizers of Singularly Perturbed Functionals with Nonlocal Term

Tzoukmanis, Niko

Paperback

Series: Augsburger Schriften Zur Mathematik, Physik Und Informatik, Book 7

General MathematicsPhysics

Currently unavailable to order

ISBN10: 3832506500
ISBN13: 9783832506506
Publisher: Logos Verlag Berlin
Published: Aug 12 2004
Pages: 154
Weight: 0.40
Height: 0.40 Width: 5.68 Depth: 8.04
Language: English
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.

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