Near-Periodic Local Minimizers of Singularly Perturbed Functionals with Nonlocal Term
Niko Tzoukmanis · SIAM Journal on Mathematical Analysis · 2006
We consider singular perturbed functionals with a nonlocal term which are a one-dimensional model for an austenite/twinned martensite interface. The parameter range is chosen in a way that a limit functional can be derived. By examining the limit problem, we show the existence of highly oscillating, near-periodic minimizers of the original functionals which are close to periodic sawtooth functions.