Local Minimizers of Singularly Perturbed Functionals with Nonlocal Term
By (author) Niko Tzoukmanis
Paperback (Published)
(August 2004)
ISBN: 9783832506506
5.75 x 8.31 inches
Price: $61.00
On back order
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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Connecting Atomistic and Continuum Models of Nonlinear Elasticity Theory
Rigorous Existence and Convergence Results for the Boundary Value Problems
Volume 31
The Lifted Root Number Conjecture for small sets of places and an application to CM-extensions
Volume 12
Effective Theories for Brittle Materials
A Derivation of Cleavage Laws and Linearized Griffith Energies from Atomistic and Continuum Nonlinear Models
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